Class 10th Mathematics CBSE Solution
Exercise 11.1- Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure…
- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar…
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle…
- Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then…
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then construct…
- Draw a triangle ABC with side BC = 7 cm, B = 45, A = 105. Then, construct a…
- Draw a right triangle in which the sides (other than hypotenuse) are of lengths…
Exercise 11.2- Draw a circle of radius 6 cm. From a point 10 cm away from its centre,…
- Construct a tangent to a circle of radius 4 cm from a point on the concentric…
- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended…
- Draw a pair of tangents to a circle of radius 5 cm which are inclined to each…
- Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of…
- Draw a circle with the help of a bangle. Take a point outside the circle.…
- Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure…
- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar…
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle…
- Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then…
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then construct…
- Draw a triangle ABC with side BC = 7 cm, B = 45, A = 105. Then, construct a…
- Draw a right triangle in which the sides (other than hypotenuse) are of lengths…
- Draw a circle of radius 6 cm. From a point 10 cm away from its centre,…
- Construct a tangent to a circle of radius 4 cm from a point on the concentric…
- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended…
- Draw a pair of tangents to a circle of radius 5 cm which are inclined to each…
- Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of…
- Draw a circle with the help of a bangle. Take a point outside the circle.…
Exercise 11.1
Question 1.Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts.
Answer:Step 1: Draw line segment AB = 7.6 cm
![](data:image/jpeg;base64,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)
Step 2: Draw a ray AC making an acute angle with line segment AB .
![](data:image/jpeg;base64,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)
Step 3: Along AC, divide (5+8) 13 equals points
A1,A2,A3,……………….,A13 on AX such that
AA1=AA2=A2A3 and so on .
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Step 4: Join BA13
![](data:image/jpeg;base64,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Step 5: Through the point A5, draw a line parallel to BA13 (by making an angle equal to ∠AA13B) at A5 intersecting AB at point D.
C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8.
The lengths of AD and DB can be measured. It comes out to 2.9 cm and 4.7 cm respectively.
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Justification
The construction can be justified by proving that
![](data:image/png;base64,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)
By construction, we have A5D∥A13B. By applying Basic proportionality theorem for
![](data:image/png;base64,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)
From the figure, it can be observed that AA5 and A5A13 contain 5 and 8 equal divisions of line segments respectively.
![](data:image/png;base64,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)
On comparing equations (1) and (2), we obtain
![](data:image/png;base64,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)
This justifies the construction.
Question 2.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are
of the corresponding sides of the first triangle.
Answer:Step 1: Draw a line segment AB of 5 cm.
![](data:image/jpeg;base64,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)
Step 2: Taking A and B as Center, draw arcs of 6 cm and 5 cm radius respectively. Let these arcs intersect each other at point C. △ABC is the required triangle having length of sides as 5 cm , 6 cm , 7 cm respectively.
![](data:image/jpeg;base64,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)
Step 3: Draw a ray AX making acute angle with line AB on the opposite side of vertex C.
![](data:image/jpeg;base64,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)
Step 4: Locate 7 points, A1,A2,A3,A4, A5,A6,A7( as 7 is greater between 5 and 7), on line AX such that AA1=A1 A2=A2 A3=A3 A4=A4 A5=A5 A6=A6 A7
![](data:image/jpeg;base64,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)
Step 5: Join BA5 and draw a line through A7 parallel to BA5 to intersect extended line segment AB at point B′.
![](data:image/jpeg;base64,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Step 6: Draw a line through B′ parallel to BC intersecting the extended line segment AC at C′.△AB’C’ is the required triangle.
![](data:image/jpeg;base64,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Justification
∆AB' C'~∆ABC
by AAA Similarity Condition
![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAAAqCAMAAAApilEOAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpCQZpC2ZrbbZrb/kDoAkDo6kGYAkNv/tmYAtmY6tpA6ttv/tv/btv//25A625Bm27aQ2////7Zm/9uQ/9u2/9vb//+2///bWf9wmwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADCUlEQVRYR+2Za3fTMAyG4+5CYEC5l46FXQJLS/L/fx+SZTvKassSn3o48YduO/WjvJZkJ3nXNOs4wwyM2+vnuqyTWTqMB7YTkqxD+72uujmZpcN4ZDsR6GlPiZ32DsfmLf41XDxJsgMTZ/3+BNwNcAK2CN9oiKb3gly+7oPb3HmJ4/YViL938Nn0+FEegQmzevfuebrHKBK2CK8iOqx4qRzd1/a9FzjtUatvtmkv9wgxYdahRW66vZMxFl5JeFV9vu7jx8fUJSQbPscv4oYMTJjVh2pVsCgbwisJagHK6csBdQ0L8nH//LgSu5oykBhfJHkfxAvO4bWEv1TKyUI4Fjq0D22a6wexq6mbEhO7qsrELY/hDYceleh0HN5gJ/vv/I+pyy+Pk4wxyY7hDbIHl99kdMj4MrM9IyePMdYm8Zk2NEmXP/3GD3j40ZpIdj0mZ3B9ivqkYlJ4JYGnX35DDn41/vRQZ5szqGdwGBsPQHGwYioJyEh+t4euHrf4Nd0POi9CGAuG0rjZwW2qtidYeCVROv3Grb914o+Lp3D3vdzJqhcMTZ1+ts5dfpOfvRbhVQTUsZYKWer67ZqBNQNrBl5kAA7Nyo3hLFNmk93RixG+rZkWa+cMRNKU+aWUc4nB7wqcgFWJsyy/RlSPjxxHlQviwxlKt7i8nRMJq2xNKtY5/08GfhVPsGAyLY2j6sKjndXMHlPtSZ35XgroAM/D0sEbjSluHFVVw1tNOMpnV6oC5Y2pIlTzB6MxpX4JpkMm2Fmzx1RbataYKkMV2cmYYsZRTQG8w0U7q+DAZCJkjal/lp1MJr0vBdeKVP1VPwkzGlNytmeTSe1LgZBEGcyaOb4KOrSvW3dVOkhmk0ntS4HsRKkUUMLn+Cpout01x+Lz6mwyWbZkoqxNYjSmSg4PM5m0vhQkjlFqj4n7XmqIrKfTwUwmQ7YZpfaYuO+lgTo0mgrZ5iaT0peKXYpGFthZWo9p4XtpIKzIMe+ec5Ppkf7pVPOlsEW4naVzpfxaWXyFMXX8DPNvHprmL731YR7f+/zvAAAAAElFTkSuQmCC)
Question 3.Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are
of the corresponding sides of the first triangle.
Answer: 1. Now in order to make a triangle, draw a line segment AB = 5 cm.From point A, draw an arc at 6 cm. Draw an arc at 7 cm from point B intersecting the previous arc.
![](data:image/png;base64,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)
2. Join the point of intersection from A and B.
![](data:image/png;base64,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)
Hence, this gives the required triangle ABC
3. Dividing the base, draw a ray AX which is at an acute angle from AB
![](data:image/png;base64,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)
4. Plot seven points on AX such that:
AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7.
![](data:image/png;base64,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)
5. Join A5 to B.
6. Draw a line from point A7that is parallel to A5B and joins AB’ (AB extended to AB’).
7. Draw a line B’C’ || BC.
![](data:image/png;base64,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)
Hence, triangle AB’C’ is the required triangle.
Question 4.Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are
times the corresponding sides of the isosceles triangle.
Answer:△A′BC′ whose sides
of the corresponding sides of can be drawn as follows.
Step 1 Draw a △ABC with side BC = 6 cm, AB = 5 cm and ∠ABC =
.
![](data:image/jpeg;base64,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)
Step 2 Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
![](data:image/jpeg;base64,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)
Step 3 Locate 4 points (as 4 is greater in 3 and 4), B1,B2,B3,B4 on line segment BX.
Step 4 Join B4C and draw a line through B3 , parallel to B4C intersecting BC at C′
![](data:image/jpeg;base64,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Step 5 Draw a line through C' parallel to AC intersecting AB at A'.△A′BC′ is the required triangle.
![](data:image/jpeg;base64,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Justification
∠A=60° (Common)
∠C=∠C'
By AA similarity condition
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAAApCAMAAADgQyBwAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjqQZpCQZpC2ZrbbZrb/kDoAkDo6kGYAkNv/tmYAtmY6tpA6ttv/tv/btv//25A627aQ2////7Zm/9uQ/9u2/9vb//+2///bcwqkpgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACY0lEQVRYR+2X607DMAyF2wHbuI3rVmCMrbSD5v1fENtpLtOS2I0mTUL1DwTinNpxUjdfUYzxXzugqmkDa1NViTG5xT+YONR+P4HtRmDDJJQLgjW15eQDhd1iBr5NCT/Z8LV1edeojX4GFyZXwZvWL/N7fJyqsKBuYdaTSuFp93O0qTdRWSYXb+oet2YXdVmSbpmyQFvL+kSLtLl4Uz0r6oud6dbv+xX+zgWVRVpVkVkWJhdvUtWq2M9XVBYe+emXJIPTyjZdP9Pm4k3766Y/VdQBtRbtidPyGdwybS7eVNNYwI3IO/L8friybC7W1D3gG9SWsIu6LNbRb4fVytpLB97l4kwtjQM9hvIGRFvieJEMCC8XY9KlQFmwi7q2NWXhwtOqarKEKcwfST9X2tQt4NVroCA4XVv98blcciXZl7bXqs852F65j4+fC+aKzCSoZZSMHRg7cLIOwMAQXYxOllD2oGFlrWmU0V162GKyjbAKmzPwS2yRKQ/9L2JM+GT9PIOqxg/ej+i2TtVl78Uw49CyztC5MeXwDhjMPeDkxFU7qDOEzFzRA0gdc1jM9TlZk1A4AjpLyCkfPC2A1DGHwdyDK3ObQD//aq11jpBTPnyve3z3kDrisJhry8JLNFBmNDye7nWOkFO+MFJHHBapdVmaqZEy02X5OodKSR8tlvDdY6uIwyG1z9Tdc+Je7rG31rlTm/QFkTricEituyVg6iMdT8i681lILabEI5qU8S7socF31uBhrpipj9mbI2TdrDykzu8WjCMJVuchtZipj9lbhNV5SL3rPyosU4d0AkJOIfUfgLVSV1yL1nAAAAAASUVORK5CYII=)
Also, ![](data:image/png;base64,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)
AB’=
AB ,B’C’=
BC and AC’=
AC
Question 5.Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ ABC = 60°. Then construct a triangle whose sides are
of the corresponding sides of the triangle ABC.
Answer:Given in Δ ABC,
- Length of side BC = 6 cm.
- Length of side AB = 5 cm.
- ∠ ABC = 60°.
Steps of Construction:
- Draw a line segment BC of length 6 cm.
![](data:image/png;base64,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)
2. With B as center, draw a line which makes an angle of 60° with BC.
Construction of 60° angle at B:
a. With B as centre and with some convenient radius draw an arc which cuts the line BC at D.
![](data:image/png;base64,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)
b. With D as radius and with same radius (in step a), draw another arc which cuts the previous arc at E.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWYAAABnCAMAAAAE0xg1AAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAgdQTFRF////l5eXYWFhsbGxhoaG9vb2ampq3d3d+Pr97fP64ev31uT04Or3sczqf6vdap3XX5bUU47RSIfORITNts/rjLPgWpLS2+f1m73kY5jVZ5vWeqfbjbTgoMHls83rx9rwwNbugKvdRYXNeKbbqsfo1eP06PD5+/3+5OTkfX19ODg45u74pcTnZZrWaJzWytzx+fv9e5KsCwwMLi4uSEhIk7jiSojOhK7e4uz3DBIZQUFBrcnpWJHSg67e1OLzWneYFxsgyNvwc6PZdqXaxtrwgYGBMDAwaZzXudHsh42TJigqW5PTq8jo/P3+uNDsSHq1AwQFWVlZibLf7vT6o8LmIUBjGh0fTk5OjrTgj4+PGBgYFRUVeafbrMnp0tLSY5nVTYrPy93xTovPXpXU9fj8VI/RdaTaocHmlbnjh7DfqMbobJ7XsszqUY3Q+Pv9vNPt3un24+33U43Rw9fvsMvqZJnVYpjVkbbh3Oj2r8rqg63eV5DSfqrcr6+vK0lsI0RqR2uThISEGx0gHSs6DDJcCzFcECI3XYCoJUhwJ0pww8PDEjVeBggLD0eIFWXA8vLyRkZGEhQWKissKSstFxgYLy8vGig3mZmZ39/fq6urFhYWDjFZQ0NDKysrKioqdHR07u7u6vH5On3Kmr3kzMzMvtTtWZLSdKTa1OPzJ3HFOX3Kc3Nz8PX7QTe8bwAAAAFiS0dEAIgFHUgAAAAJcEhZcwAADsMAAA7DAcdvqGQAAATPSURBVHja7Z35WxNHHMYjeMsVX46AMQKB4MXhCYqgoHiB931f8UJFlN4tbYHeKKa2ar2qYCX0+CM7YXcptKHZWR/my+58Pz+Qye687Ltv9pmd2Scz8fkYhmEYhmGmJzPSDNKpjXibGTNnUVvQAY5ZCRyzEjhmJZi3wNlzqI14G76alcAxK4FjVgLHrASOWQnWYJvTZhiGYbzH3HnzFyyYP2+urILat1vIyMzKzvEvhMlCf052VmaGbQW1fTeQkZuXj6Tk5+Vm2FJQn8K0pyBQaGXlL1oUXBxasiS0OLioyG9tLQwUpFRQn8R0p7hkNK7ScFl5pGLiropIeVm4dHR3SbHPt3TZ8uXLlv6vgknKipWVicSqAtU1k1WpqQ5UJepUrlq9Zu3aNatXpVQwE4msWy8Sqw3VpapYF6oFNmxMDLM3brClYMao3yRCbmi0V7lx8xbjccaWzTYVTIKmZhHy1m2267dsN2Le3kLt3E0ERcg7dkoIdu02Yt69i9q6mwBa2/ZI1N+7b/+BRMoH9u/bS+3dReDgIZnqh4EjR4+lpR07egQ4TG3ePQSkah8XTUzgxMlTp06eCIjicWr33uS0iPaMeD17Vvw5I96cpnbkRc4B5y/88/bCeeActSfvcRG4FB2/IXoJuEjtymtcBsL/3hYGLlP78hZXgKv/3XoVuELtzEtcA64n234duEbtzTu0AzeS77kBtFO78wo3gVsdyXd13AJuUvvzBrdFF7lzsp2dYudtaode4M5doGvy3V3A3TvUHj1AMEXzKxruILVH99OUMkXxOTRRu3Q9zWhN8RTvUCuaqV26nXqgLVWdNqCe2qcG7NmBTRFqExqwE1hH7UEHtmL9CmoPGrANWEntQQcaUEltQQcagWJqDzrQgBJqCzrwHlDw7v+FSUEnIPdtBMYR7+MDags68CHwEbUHDegCPqb2oAEdpfiE2oMONONTags60M6NswrK+amzCiLAZ9QeNKACyKb2oAN+5FBbcB/dn3/xpZyiCH5q00R09/R0OxKm9/Z99fU3vVJLB3/73fc/UJ8wBSKr/v4+uaxM5b37A4L79+xrH8R+fPjTz7EH1CetHAdZWfSOKoW217Yk9igxk+1RjPqsleMgK5PuvgGTx09+scfTZ8a8zGdPbQq8wpPHVlZ9su1zT78lff6ixR6xl0bMv8ZsCrzCi+dWVv096mJ+yTFzozEFvEOjwbdACZzfAp126B5yh05Sy8MT2zgfnvh4sC2D48G2E/jRkQr4QagSIkCWUTKW0X71mtqRJykHMo2SsSh8Ov8uylRQBpjriJpr72u2BP/gkOjWvZnyw4SRb5bMfOfM/o361BXyZuBtIurhqG1FfHRUMzQodZiaUuSZRTPm1680+kHBkd/fGi/2r+f46EcSH5I6TjWQaxbNmGfN1ChmIzNftFpWMvKH1HECY02zjjFHh+VbZSvmERlRFQqtooaNxuCQ05jjUsK6cV8jt26Bf+rTo3MUs/FkLy6jCY2bFKFhh855oyF6KH/Z19SOm+Kj4/DEvAWOvdqWRIclLucJE9Z0HGw77tBJxczTLx0MT8yY7X8wPJk4cSFLDrbNtlliGMhT4x0gPdjmhR5UwMuWKIEX4VEBLymlhIO8QJoCArzc32T8DUoKJyXV4OSFAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDE5LTA3LTA4VDEwOjA3OjQyKzAwOjAwgTns1wAAACV0RVh0ZGF0ZTptb2RpZnkAMjAxOS0wNy0wOFQxMDowNzo0MiswMDowMPBkVGsAAAAASUVORK5CYII=)
c. Join BE. The line BE makes an angle 60° with BC.
![](data:image/png;base64,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)
- Again with B as centre and with radius of 5 cm, draw an arc which intersects the line BE at point A.
![](data:image/png;base64,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)
4. Join AC. This is the required triangle.
![](data:image/png;base64,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)
- Now, from B, draw a ray BX which makes an acute angle on the opposite side of the vertex A.
![](data:image/png;base64,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)
6. With B as center, mark four points B1, B2, B3 and B4 on BX such that they are equidistant. i.e. BB1 = B1B2 = B2B3 = B3B4.
![](data:image/png;base64,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)
7. Join B4C and then draw a line from B3 parallel to B4C which meets the line BC at P.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZoAAAHoCAYAAABw7CmpAAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAZiS0dEAP8A/wD/oL2nkwAAAAlwSFlzAAAOwwAADsMBx2+oZAAAgABJREFUeNrs3XV4HNe9//H3zDKLGWyBSbZlW2aIOXEYmlKaNoUUU25vGXLLt73tr71lhjRt2jTMZmZmWWgxa7WMM78/1nbixEkMkmYlndfz+Gkjr3a/M5b2s2fme86RVFVVEQRBEIQhImtdgCAIgjC6iaARBEEQhpQIGkEQBGFIiaARBEEQhpQIGkEQBGFIiaARRixvMMZ7fnmcwo9tY+upfkT/pCAkJxE0woikqtDUG6LbG2VuuZM/bmrFH45rXZYgCJcggkYYkeKKyt+3deC06LhnYQ576zyc7QmKUY0gJCERNMKI1O2JsKPazdIpaSyYkILLomdPrQdFJI0gJB0RNMKIE1dUTrX66fJEWDzRRU6KkbllLrae6icYEZfPBCHZiKARRhxFhfXH+6gotFGaZUWWJG6ckc6LR3rZXy9GNYKQbETQCCOKosKpVh8vHO7h0zcWYTPrAFhTmc6yKSmsO9ZHXBm812toaKCpqUnrwxaEEU2vdQGCcCXiisruWg91nUHu/cVxTPrEZyUV6PdFac0P0+uNkJNiuubXamtro6amhtLSUq0PWxBGNBE0wojiC8bYWe3mnYty+NJt44grL18mq+8K8sm/VHOmPUCWy4gsSVf9Ol1dXbz00ku4XC4yMzO1PmxBGNHEpTNhxFBVaO4LcbDBy11zMhmfZaEsx3rhz+KJKUwpsPH37e14g1ffFNDV1cW6deuoq6sjJycHp9Op9aELwogmgkYYMcIxhUd3d2EzycwY53jN31tNOpZXpLHrzMBVz6np7Oxk/fr1nDlzhoyMDDIyMrQ+bEEY8UTQCCNGa1+IZw90M2u8k2zXpe/BLJ7oos8fY/PJfiJX2BXQ1dXF+vXrqa2tJR6Pk5OTQ1pamtaHLQgjniR22BRGilBEobYzQJrdQF7qpYMmElOobg+Q4TCQ7TIhX+ZtmldeLlNVlVAoxPXXX8+yZcuQruFejyAIohlAuAJHW46Rn5JHuj1dk9c3G2WmFtrf8DFGvcy0N3nMq706ZFRVJSUlhaysLBEygjAIRNAIl+3Zw8/R5+9jesF0phVMZWrBVAy6kf0j9OqQkSSJeDxOdna2uGwmCINkZL9LCMOqzd1OXVcdHQOd7G/cT15KHpPzJlGRX0FZ1siba9Ld3c369esvChmAWCxGTk4OqampWpcoCKOCuEcjXLY99Xs53HSE460naO5rBhXS7GmkWlMZnzmeivzJTMmbQrYzS+tS31R3dzfr1q2jtrb2opA5/+tw++23M2PGDK3LFIRRQQSNcNkUVWEg6MEdcHO67TTHW09wvO0kvd5eLAYz6Y500myplGWVMa1gKlPyJmMz2bQu+zUudbnsvPPdZjfffDNFRUValyoIo4IIGuGqRONR+vx9tLvbOd1ezYnWU1R3VOML+XBZXWQ6MslLyWNCTjnTCiooyypLihvrXV1dbNy4kVOnTiFJEjqdjlf+CkQiEebMmcPy5cvFRE1BGCQiaIRr5g/76fX1Ud9dz+n205xqO01TXzNxJU6aLY0sZyYTcyYwt2QuE3MmYtQbNKvV5/PR1dXFsWPHOHHiBF6vF6PRiE6XWJwzHA5zxx13MGfOHK1PqyCMGqIZQLhmNpMNm8lGUXoh0wun0ePtpaarlhMtJzjZdopjLcdp6mvmZNspyrPLqRo3i4r8KViN1mGv1W63Y7fbKS4upr29na6uLsLhMDabDZ1OR3p6Ounp2rRvC8JoJYJGGFRptjTSbGmUZpUwq3gm9V31HG0+xpGWo1R3nKGpt5lTbacoyy5jZvEMKvIrSLWmDHudLS0tRCIRjEYj2dnZKIpCf38/ubm5uFwurU+jIIwq4tKZMOT6/f3UdNVyrPk4R5qPcrb3LDpJR05KDmXZZVQWTqcibwo5ruxhq+kf//gHNTU1WCwWVq9eTWpqKgcOHGDcuHFMnz4dg0G7y3uCMNqIoBGGjTfopa67nhOtJzjUdISGngZi8RhZjixKs0uZll/B1IKpFKcPbbfXrl272Lp1K/39/SxcuJBVq1ZhtVpxu90YDAZstuTrlBOEkUwEjTDsgpEg9T0NnGw7xaHGQ9R11xMIB0izp1GWVcqk3InMKJpBSeZ4dLJuUF/b5/Px17/+lfb2djIyMrj99tsZP3681qdEEEY1ETSCZqLxKA3djVR3VLO/8QB1XfX0B9w4zQ7Kskspyypj9rgqSrNKMBvMg/Kazz33HIcPHyYSiXD99dczd+5ccZlMEIaYCBohKdR3N1DdXs2Bswep66qn09OFxWCmPLuMsuwyZo+bRUlmCU7L1c9taW1t5Z///Cd9fX2UlZVx2223if1mBGEYiKARkkpzXzOnzwVOfVcDrf2tGPRGSjLHUZ5dzpLyxZTnlGPSG6/4uR9++GHq6uowGAzcdtttTJ48GVkWWzIJwlATQSMkpY6BDk61n+ZAw0Eaeho523sWg85AeXYZ0wqmsbBsAaVZJa/7/e1trdTVnqG3r5/UFBehcJSjx47R3+9m9uzZrFmzBovFovVhCsKYIIJGSGq9vl5Otp1id90e6rrqaHW3YdAZqCyczrySuUwvnEZeSt6FxyuKwlNPPs6mzds41DBAlydCmsNEvKea/JxMFi1azFvf9jaKioqSYkkcQRgLxIRNIaml29NZMmExU/MrONR0mO1ndlDf3cCBxkPUdNZR2XKcZZOWUppVQpotjV/98pf8z+8fw2stJ+Kahi41heawD1Qzpw7vJy2zjhSXS4SMIAwjMaIRRpSWvhYONR1mZ+1uGnoaCISD5KTkMKNoOgWxPN7/oa8SKr8XS+lSEndfFEACvYVQ006MJ/7Kn/7f17jxxjXoNVxzTRDGEhE0woh0uv00u+r2cqz5KA09jSiqwrG/HKHffjOGKW8DRQFe9aNtdBA79ncWZnTwy598j+LicVofhiCMCaLlRhiRJuVO4r5F93LP/HeyqGwhuc5cmk61IBcuAyXOa0IGIOqHwuvYtOsw/X19Wh+CIIwZ4h6NMGLJkszs8VVMyp3I9pM7+EPst8jWVEDikkGjqujtmfS7vcSiUa3LF4QxQ4xohBHPbrazZtYN2O0OlEA/lwwZAEki5u3CkZ6CwXjl83AEQbg6ImiEUWPZ8hXQtBEkOfHnlSQJSW8hULueFQtnkZGRqXW5gjBmiKARRo3PfvpTFIQOE+84DEoUZAPI+sT/qirh9qPIbS9RtagU2Tq4i3UKgvD6dA8++OCDWhchCIOhuLiYuppqarY/itsfRopHUEJupEAXwZaDmBr/RuFUA6aJFoJqkFxXLk6LQ+uyBWHUE80AwqgRi8WYVjGZ1qYGjh56glTzJKI6J4T6cbfVUrGkksKVJXQFu3nywFOEo2FumHo9RWmFWIxiORpBGCpiHo0wauzevZu1a9ciyzKLFi0iIz0Nv8/Ljp27iCsK4UCY5XevZEfLLs60naHH10NRWhFLJixiTskcClILMOjEZy9BGGzit0oYFfx+P88//zyyLONyuaisrCQtLQ2A6po6GhsbiUQjZOszuX/h+9nVsIv1JzfS0tfC33b+nQNnD3F9xSqmFUwlw5GBLInbl4IwWMQ9GmFUeP755+np6UGWZVatWsX48eMvrGeWn59PU1MT4XCYvfv3kpGSzso5K3FZXfT73cSVOO3udg6ePUxrfyvptnQynZlIiPXQBGEwiKARRrzu7m6efvppVFWlpKSENWvWXLRops1mw+l00tLSQjQapbWtlczMTGaUz6CycDomg5lAJEAwEqSuu57m/hacFgdp9jSMOrEemiBcKxE0wogWi8V46KGHCIVCGI1GbrjhBlJTU1+zOnN6ejo6nY729na8Xi/d3d2UlJSQnpLO5LxJTMyZSEyJEYlFaOlv4XDTEdwBN6nWVFKsYrVnQbgWImiEEe348ePs378fgKqqKubNm/e6oZCXl4fP56Onp4fOzk7GjRtHWloasiyTYnVRNW4WxelF9Pp6aR/o4HjrSeq763FZU8hyZqKTdeJymiBcBRE0wogVCAT47W9/i16vx2azcfPNN2O1Wt/we8aPH09zczM+n4/9+/cTjUbJy8vDZDIBkOnMpDC9kD5fH76wjx5fL0ebj9Dn6yfdli5GN4JwFUTQCCOSoihs2LCB9vZ2dDodK1asoLy8/E2/T5IksrKyaGlpIRwO09raitPpJCcnB50usVpAqi2VWeNm4jA7cAf66Qu4OdF6gjOdNaRaU8hNyRVdaYJwBUTQCCOSx+PhkUceQa/XU1BQwC233HLZ32u327Hb7bS3txMMBuns7CQnJ4f09PQLjzHoDJRnlzEpdxI9vl4GggP0B/o51nKMYDREfmq+mOQpCJdJBI0w4kQiEf75z3/i9/sxGAzccMMNZGRkXNFznH98Z2cnbrebvr4+srOzcblcFz3OZXVRVTyTFKuLXl8fPd4eznTW0DHQQW5KLqm2VK1PhyAkPRE0woiiqir19fVs27YNvV5PZWUlCxcuvKrnKigoIBAI0NPTQ3d3N6FQiPT0dOx2+0X3YQw6A2VZpZTnlNPp6aLL00VDdyNnOs+Q6cgkLyVX69MiCElNBI0wogQCAX73u9+h0+kwmUzccsst2Gy2q36+kpISPB4Pvb29dHZ2sm3bNjIzM8nNfW14pFpTmJI3GV/IR7evm1A0TF1XHQ6zg8K0Qq1PjSAkLbEEjTBixGIx9uzZg6IoGI1GFi9eTFZW1jU/74QJE2hsbKSjo4PMzExk+fVv9Gc6Mnhg5Ud5YOVHtT4dgjBiiNYZYcQIBAJs2LABvV5PdnY2ixYtGpTnLSsrY8GCBaSlpeH1etm2bRv19fVaH64gjBoiaIQRIRgM8tRTT2EwGNDr9Vd9X+b1zJw5k1mzZmGz2ejo6GDbtm20t7drfdiCMCqIoBGSnqqqdHR0UF1djV6vZ9KkSUyZMmXQX2fJkiVMmjQJg8HAmTNn2LlzJ263W+vDF4QRTwSNkPS8Xi//+te/MBgMGAwG5s+fPySvI0kSCxcupKioCJ1Ox5EjR9i3bx+RSETrUyAII5oIGiGpRaNRjh49emHOzPz58y/ZETZYsrKyWLJkCbm5uaiqyqFDhzhx4oTWp0EQRjQRNEJS8/l8vPDCCxiNRjIzMwetAeCNvLI5wOPxsGvXLmpra7U+FYIwYomgEZKW3+9n3bp16HQ6DAYD8+bNQ68fno78GTNmMHfuXKxWK+3t7ezYsUM0BwjCVRJBIySt7u5ujh49islkory8nOnTpw/r68+dO5epU6cCUFtby/bt2/F4PFqfFkEYcUTQCEmpv7+fJ554Ap1Oh9FoZN68ecNew/lRVHl5OYqicPr0aXbt2kUsFtP69AjCiCKCRkg60WiUM2fO0Nvbi9lspqqqioKCAk1qyc7OZuHChRQUFBAOhzl+/DhHjx7V+hQJwogigkZIOm63m+eeew6DwUB6evqgT868UmVlZSxcuJDU1FTcbjd79uyhpqZG69MkCCOGCBohqfh8PrZv346iKFgsFubMmYPZbNa6LCorK1m0aBEGg4H29nZ27txJR0eH1mUJwogggkZIKl1dXRw8eBCz2UxJSQkzZ87UuqQL5s+fz8qVK9Hr9dTX17Nu3To6Ozu1LksQkp4IGiFp9PT08OKLLwJgsViYPXu21iW9xrRp06ioqCASiVBXV8fmzZsJBAJalyUISU1sEyAkhVgsRkNDA62trTgcDiorKxk3bpzWZb2G0+lk/vz5eL1ezpw5Q11dHTt27GD16tVX/FxxJc6W6q08tPNhZCnxmW/55GXcM/8dF/5bEEYDETRCUujs7OSFF15Ar9eTnp4+ZOuZDYb8/HwWL16M3++nvb2d48ePk56ezqxZs67oeXSyjvml85icN/nC12xGqwgZYdQRQSNozufzcfDgQYLBIGlpacycORO73a51WW+orKyMYDDICy+8QH9/P3v37sXlclFaWnpFz2M1WrEarVofjiAMKfHRSdBce3s7+/fvx2q1Mn78+KS8N3MpU6ZMYcmSJUiSdGEPm56eHq3LEoSkI4JG0FR3dzdbt24lGo3icDiSqsvszeh0OqZMmUJlZSWhUIimpibWr19PKBTSujRBSCoiaATNKIrC2bNnaWhowOFwMGXKlCu+9KQ1l8vFvHnzmDhxIsFgkIaGBrZv3651WYKQVMQ9GkEzTU1NrFu3DkmSyMjIYM6cOVqXdFXy8/NZsWIFiqJQX1/P4cOHMRqNXHfddVqXJghJQYxoBE34/X5OnjyJ2+3G5XIxffp0UlNTtS7rqhUXF7N06VKysrIYGBjg4MGDHDt2TOuyBCEpiKARNNHU1MSBAwew2WwjqgHgjZSWlrJy5UrMZjNut5udO3fS1NSkdVmCoDkRNMKw6+7uZt++ffj9flJSUpg2bRo6nU7rsq6ZJElMnDiRJUuWEI1G6ezsZOPGjbjdbq1LEwRNiaARhl1DQwO1tbU4nU4mTpxIeXm51iUNGoPBQGVlJdOnTycYDNLc3Mz69euJRqNalyYImhFBIwyr+vp6duzYQSwWIysri1mzZiFJktZlDSqXy8XixYsZP3484XCYmpoadu3apXVZgqAZETTCsAmFQpw+fZqOjg5SU1OpqKggMzNT67KGxPlOtPT0dILBIAcPHuTUqVNalyUImhBBIwyburo6jhw5gtlsprS0lKqqKq1LGlKlpaWsXr0ao9HIwMAAW7Zsoa2tTeuyBGHYiaARhkVvby+HDx+mv7+f9PR0KioqMBqNWpc1pCRJYvLkySxatIhIJEJXVxfr1q3D4/FoXZogDCsRNMKwqK6upqamBpfLxaRJkygrK9O6pGGh0+moqqqioqKCcDjM2bNn2bhxI7FYTOvSBGHYiKARhlxDQwOHDh0iGAySk5NDZWXlqGhnvlxOp5OlS5dSUFBANBrl1KlT7N27V+uyBGHYiKARhlQkEuHkyZO0tLSQlpbG5MmTyc7O1rqsYZefn8+qVatwuVyEw2H27t1LbW2t1mUJwrAQQSMMqerqak6ePIler2fixIkjanXmwVZeXs7q1auRZRm3282GDRvo7OzUuixBGHIiaIQh43a7OXbsGN3d3WRmZjJ58mQsFovWZWmqsrKSFStWoNPpaG9vZ+3atXR3d2tdliAMKRE0wpA5fvw49fX12O12Jk2axPjx47UuKSksXLiQyspKYrEYtbW1rF27Fr/fr3VZgjBkRNAIQ+Ls2bMcP34cj8dDfn4+06ZNG/XtzJdLluULKweoqkp1dTU7duwgHo9rXZogDAkRNMKgUxSFo0eP0tzcTEpKCpMnTyY3N1frspJKWloa119/PZmZmciyzP79+zl69KjWZQnCkBBBIwy6EydOXOiomjJlCtOnT9e6pKRUWFjIqlWrsNlsRCIRtm7dSnNzs9ZlCcKgE0EjDCq/38+RI0dob28nMzOTiooK7Ha71mUlrcmTJ7N48WL0ej19fX289NJL9Pb2al2WIAwqETTCoDpw4ADNzc3YbDYqKiooLCzUuqSkt2DBAiZPngwkNoTbsGGDaA4QRhURNMKgaWlp4dSpU7jdbgoKCqioqMBsNmtd1oiwfPly8vLykGWZI0eOsHfvXrFMjTBqiKARBs2BAwdobW3F4XAwefJkcnJytC5pxEhLS+OGG27A5XJhNBrZtWsXNTU1WpclCINCBI0wKE6cOEFjYyOxWIyKigqmTp2KLIsfrysxbtw4li5dislkIhKJsGXLFjo6OrQuSxCumXgnEK5ZJBJh3759tLW1kZ6eTmVlJU6nU+uyRqRZs2Yxc+ZMdDodra2tbNiwAbfbrXVZgnBNRNAI12zPnj10dXVhNpuZPn26uGR2jVauXElhYSF6vZ4TJ06wc+dOgsGg1mUJwlUTQSNck87OTk6cOEFfXx8FBQVMmzYNq9WqdVkjml6v54YbbiAjIwOTycSePXs4duwYiqJoXZogXBURNMI12blzJ52dnVgsFqZNm0ZmZqbWJY0Kubm5rFy5EqfTiSRJbN26laamJq3LEoSrIoJGuGqnT5+mqamJcDjM1KlTmTx58pja0GyoTZo0iQULFmCxWBgYGOCll14S2woII5IIGuGqqKrKtm3b6OzsxOVyMWvWLFwul9ZljTrz58+nsrISm81GU1MTmzdvpqenR+uyBOGKiKARrsrOnTtxu93o9XpmzpxJVlaW1iWNWmvWrGHSpElYLBYOHz7Mxo0bRSeaMKKIoBGuWF9fH4cPH6a/v5+8vDxmzJiBzWbTuqxRbfny5WRlZWGxWDh48CD79+8XnWjCiCGCRrhiW7Zsob+/H4PBwMyZM0lNTdW6pFHP5XJxww03kJaWhsViYefOnVRXV4s9bIQRQQSNcEVqa2tpbGwkGAwyZcoUJk2ahMFg0LqsMaG4uJjrrrsOp9NJPB5n8+bNtLS0aF2WILwpETTCFVm3bh19fX1YrVbmz58vGgCG2fTp06mqqsJms9HT08OGDRtEJ5qQ9ETQCJdtz549+Hw+AKqqqsjIyNC6pDHpuuuuo6ysDLPZTG1tLTt27BDNAUJSE0EjXBav18vu3bsZGBggOzubOXPmiAYADS1fvpzs7GxMJhN79+7lwIEDojlASFoiaITLsnHjRnw+H7IsM3v2bBwOh9YljWmpqamsXLmSjIwMzGYzu3fv5syZM2KZGiEpiaAR3lRTUxO1tbUEg0EmTpzIlClTMBqNWpc15pWUlLBo0SJSUlIIhUJimRohaYmgEd7Uc889h9frxWAwXOh6EpLDjBkzmDFjBna7nc7OTrGHjZCURNAIb+jw4cN4vV7i8TizZ88mPT1d65KEV1m2bBkTJkzAZDJRXV19YdUGQUgWImiE1xUMBtmwYQM+n4+MjAwWLVoktgBIUkuWLCEvLw+DwcCBAwfYv38/oVBI67IEARBBI7yBjRs3Eg6HUVWVuXPnipBJYhkZGSxbtozs7Gx0Oh379+/n9OnTWpclCIAIGuF1tLW1ceLECUKhEGVlZUybNk00ACS50tJSFixYQGpqKn6/nx07dlBfX691WYIggka4tKeffppQKISqqqxYsQK73a51ScJlmDlz5oWVA9rb29m2bRvt7e1alyWMcSJohNc4fvw4brebWCzG7NmzxQoAI8zixYuZOHEier2empoadu7cycDAgNZlCWOYCBrhItFolOeff55QKITL5WLFihVYLBatyxKugCzLLFy4kOLiYiRJ4ujRo+zdu5dIJKJ1acIYJYJGuMjGjRuJRqPE43Hmz5+P2WzWuiThKmRnZ7N48WLy8vJQFIVDhw5x4sQJrcsSxigRNMIFnZ2dHDp0iGg0yrhx45g5c6bYAmAEKy8vZ8GCBaSlpeHxeNi9ezd1dXValyWMQSJohAueffZZotEosViM1atXi0tmo8CMGTMutKa3tbWxY8cO0RwgDDsRNAIAp0+fprOzk1gsxsyZM8nOzkaSJK3LEgbBnDlzmDp1KsCFbQU8Ho/WZQljiAgagVgsxtNPP000GsVms7FmzRpMJpPWZQmDxGg0MnfuXMrKyojH45w6dYrdu3eLbaCFYSOCRmD79u2Ew2HRADCK5eTksHDhQgoKCgiHwxw7dowjR45oXZYwRoigGeO6u7vZvXs3iqJQUFDAnDlz0Ol0WpclDIHy8nIWLlxISkoKbrebvXv3Ultbq3VZwhgggmaMe/HFF4lEIhcaAMRoZnSrrKxk8eLFGI3GC80BYlsBYaiJoBnDamtrOXv2LKqqMnXqVAoKCkQDwBhQWVnJjBkziEajNDQ0sGXLFnw+n9ZlCaOYCJoxKhaL8cQTT6AoCiaTiZtvvlnMmRkjLBYLs2fPZtKkSUQiEerq6tixYweqqmpdmjBKiaAZo/bt24ff70dRFObMmYPNZtO6JGEY5ebmsmjRIgoKCvD7/Zw4cYJDhw5pXZYwSomgGWNUVaWnp4etW7ciyzLZ2dksXLhQXDIbg8rKyliyZAkulwu3282+ffvEtgLCkBBBMwZt2rSJYDBIPB5n1apVYgWAMWzatGksX74cSZJob29n69atdHV1aV2WMMqIoBlDVFWloaGB6upqZFlmwoQJlJSUaF2WoLGKigrmzJlDMBikqamJjRs3EggEtC5LGEVE0IwhsViMJ598kng8jtFo5NZbbxVzZgSsVitVVVVMnjyZYDBIQ0MDO3bs0LosYRQRQTNGqKrK0aNH6e/vR5IkZsyYgdPp1LosIUnk5uayZMkS8vPz8fv9HD9+XDQHCINGBM0Y0dvby8aNGzEYDKSnp7NkyRKtSxKSTGlpKcuWLcNut+N2u9mzZw+NjY1alyWMAiJoxoB4PM7OnTsvrNi7bNky0c4sXFJFRQWrVq1CURQ6OzvZvHkzvb29WpcljHAiaEY5RVFoamri2LFjGAwGxo0bx6RJk7QuS0hSkiRdaA4IBAI0Nzezdu1aQqGQ1qUJI5gImlEuGo3ywgsvEIlEMBqN3HLLLaIBQHhDFouFefPmMXHiRNEcIAwKETSjmKIonDp1itbWVvR6PRUVFaSlpWldljACZGdns3TpUrKzswmFQhw9elRsKyBcNRE0o1hvby+bNm3CaDSSlpbGsmXLtC5JGEFKSkpYuXIlZrOZgYEBdu7cSXNzs9ZlCSOQCJpRKhqNsn//frq7u9Hr9SxcuBCHw6F1WcIIIkkSU6ZMYdWqVcRiMbq7u9mwYQP9/f1alyaMMCJoRiFVVWlububw4cOYzWYKCgqYPn261mUJI5Asy1RWVjJ79uwLKwesX7+ecDisdWnCCCKCZhQKBoNs2bIFv9+P2WxmzZo1ogFAuGomk4mFCxcyfvx4IpEI1dXV7N69W+uyhBFEBM0ooygKtbW11NXVYTKZKC8vJzs7W+uyhBEuMzOTlStXkp6eTjQa5cCBA5w8eVLrsoQRQgTNKNPd3c3mzZvR6XSiAUAYNJIkUVpaysqVKzEYDHi9XrZu3Up7e7vWpQkjgAiaUSQSiXDs2DHa2towm83MmTOH1NRUrcsSRpFp06axbNkyYrEYnZ2drF27loGBAa3LEpKcCJpRQlVVWlpaOHjwIFarldzcXGbNmqV1WcIoI0kS8+bNY/r06USjURoaGti0aRORSETr0oQkJoJmlPD5fOzatYv+/n6sVivLly9Hr9drXZYwChkMBpYvX05+fj6KonDs2DH27dundVlCEhNBMwooikJ9fT2nT5/GarVSUlJCcXGx1mUJo1hGRgarV6/G5XIRj8fZs2cPNTU1WpclJCkRNKNAZ2fnhbWoMjIyxBYAwrAoKytjxYoV6PV6PB4PGzZsENtAC5ckgmaEi0QinDp1isbGRux2O5WVlWRmZmpdljBGzJw5kwULFqAoCu3t7axdu/bCdhSCcJ4ImhHu/AoA5xsAZs+erXVJwhizbNkyysvLUVWVM2fOsH37drFygHARETQj2MDAAPv376ezsxOXy8WCBQswGo1alyWMMTqdjjVr1pCVlYUsy+zfv5+jR49qXZaQRETQjFCqqtLQ0MDJkyex2WwUFxdTXl6udVnCGJWZmcmqVauw2+0oisL27ds5e/as1mUJSUIEzQjV3t7O3r17icViZGVlMX/+fK1LEsa4SZMmcd1112EwGHC73axdu5bu7m6tyxKSgAiaESgajXL69GlqampwOp1UVFSQl5endVmCwNy5c5k1axaSJNHU1MSGDRtEc4AggmYkOnv2LMePH8disZCfn09VVZXWJQnCBWvWrKGoqAi9Xs+xY8fYs2ePaA4Y40TQjDADAwMcPnyYlpYW0tLSmDVrFlarVeuyBOECSZK45ZZbSEtLw2g0snv3bk6ePImqqlqXJmhEBM0I88oVAMaPH8+UKVO0LkkQXiMrK4vly5djs9mIx+Ns2bKFtrY2rcsSNCKCZgRpbW3l4MGDBAIBcnNzmTlzptYlCcLrmjp1KvPnz8dkMtHX18dLL71ET0+P1mUJGhBBM0LEYjFOnjzJ6dOncTgcTJ48maKiIq3LEoQ3tHjxYqZMmYJer6euro7NmzeL5oAxSATNCNHQ0EB1dTUmk4ni4mKxBYAwYtx6663k5uZiMpk4cOAABw4cIBQKaV2WMIxE0IwAHo+Ho0eP0tzcTEZGBtOmTcNut2tdliBcFlmWueWWW0hNTcVsNrNjxw5qampQFEXr0oRhIoJmBKitreXMmTOYTCbKysqYNm2a1iUJwhXJzc1l8eLF2O12otEomzZtEttAjyEiaJJca2srR44cwePxkJ+fT0VFhdYlCcJVmTlzJlVVVVgsFrq6uli3bp1YOWCMEEGTxFRV5fjx41RXV2Oz2ZgyZQrjx4/XuixBuGrLli2jrKwMk8l0YaXngYEBrcsShpgImiRWU1NDXV0dOp2OsrIypk+frnVJgnDN7rjjDnJycjCZTOzdu5dDhw6J5oBRTgRNkvJ6vRw5coSmpibS09OZMmUKLpdL67IE4Zrp9XpuvPFG0tPTMZlM7Nq1i9raWtEcMIqJoElSNTU1NDY2otPpmDx5shjNCKNKQUEB8+fPx+FwEAwGxcoBo5wImiTU3t7O0aNH6evro7CwkAkTJmhdkiAMutmzZzNjxgysVivt7e1s3LiRrq4urcsShoAImiR05MgR6urqMJlMTJ8+ndLSUq1LEoQhsXLlygvNAadPn2bXrl2iOWAUEkGTZM6cOUN9fT3xeJzJkyczadIkrUsShCF1yy23kJ+fj9FoZN++faI5YBQSQZNEAoEAhw4dorm5mdTUVCZPnkxaWprWZQnCkDKbzaxcuZKsrCxkWWbPnj3U1taKbQVGERE0SaS6uprW1lYAZsyYIVYAEMaM4uJi5syZQ0pKCj6fj23bttHS0qJ1WcIgEUGTJDo7Ozl8+DA9PT0UFhZSUlKCJElalyUIw2bOnDlUVlZitVppbW1ly5YtdHZ2al2WMAhE0CSJQ4cO0dTUhCRJzJ49WzQACGPSypUrmTRpEnq9nlOnTrFr1y6xrcAoIIImCdTW1tLQ0EA4HBZdZsKYd/3111NSUoIsyxw+fJiDBw8SiUS0Lku4BiJoNBYKhdizZw+tra04HA4qKipIT0/XuixB0IzNZmPJkiXk5+cTj8c5ceIEP/7xj9m5c6fWpQlXSa91AWPdyZMn6erqIhaLMW/ePNHOLAjA+PHjqaqqwu/3093dTTgcRpbF5+KRSvzLaairq4tDhw7R29tLfn4+48aNQ68X2S8IkGgOmDlzJgaDAbPZzDPPPCNGNSOUCBoNHTx4kI6ODqLRKIsWLaKkpETrkgQhqaxYsYJZs2ahqiqSJNHa2orb7da6LOEKiaDRSF1dHfX19fj9fmbOnElRUZHWJQlCUlq4cCHl5eUAHD9+nF27dhEOh7UuS7gCImg0EIlE2LFjBx0dHVgsFiorK8nIyNC6LEFISi6Xi/nz51NQUEA8Huf48eMcO3ZM67KEKyBuCFyC1+vlL3/5CydOnLjkHhmSJHHrrbdy8803X9WkyuPHj9PT00MkEmHZsmXikpkgvInS0lJ8Ph8bN26kr6+PvXv34nK5Lox0hOQmguYSVFUlGo1SVlbG/fffj06ne81jTCbTVYVMb28vBw4cwO12k5OTQ2lpKSaTSetDFoSkV1lZid/vZ9OmTXR0dLBz507sdju5ublalya8CXHp7HVIkoTBYMDpdOJwOF7zx2g0XtXzHjhwgJ6eHoLBICtWrKC4uFjrQxWEEWPBggXMmTMHRVGor69n27ZtYuWAEUAEzZsYzBVkGxsbqampwefzMWPGDAoKCrQ+PEEYUSRJYs6cOVRUVBCJRKiurmb79u1Eo1GtSxPegAiaN6DT6S552exqxGIxNm/eTHd3NwaDgTlz5ogtAAThKqSmpjJ37lyKi4sJhUKcOnWKw4cPa12W8AbEPZrXcb675ROf+MRFX5ckCYvFwsc+9rEruux17Ngxenp6CIVCrF69WrQzC8I1KC0txe/3s27dOtxuN/v37yclJUU0ByQpETSvQ5ZlJkyYwLve9a7XLH0hy/IVjUb6+/vZt28fXq+XjIwMJk6ciNls1voQBWFEmz59OsFgkJdeeomOjg527NiBw+EgJydH69KEVxFB8zrOj1wG4z7KwYMH6e3tJRAI8Na3vlXcmxGEQTJr1iw8Hg8bNmzg7NmzbNmyhZtuugmHw6F1acIriHs0b0BVVeLx+DU9R3NzM6dOnSIQCDB16lQRMoIwiAwGA7NmzaKyspJgMEhtbS3btm275t9bYXCJoBlCqqqyfv16ent7AVi0aBEpKSlalyUIo0p6ejrz5s2jqKiIQCDA6dOnOXTokNZlCa8gguYN6PX6a+o6O3bsGN3d3YRCIZYsWSJGM4IwREpKSrjuuutISUm50BxQV1endVnCOeIezSWoqorf7+fw4cO0tbW9ZgUASZIoKiri3nvvxWKxXPI5BgYG2LVrF8FgEJfLxbRp00QDgCAMoYqKCoLBIM899xydnZ1s27YNh8NBVlaW1qWNeSJoLsFut/Oe97wHn8/3utd6bTbbG64OcL4BwO/3c9ddd5Gdna31YQnCqCZJEpWVlbjdbtatW0dTUxMbN27k1ltvxWazaV3emCaC5hJ0Ot01zXNpbW3l+PHjhMNhJk6cyPjx48XugIIwDIxGI7NmzaK7u5tjx45RX1/P9u3buf76669qbUJhcIh3v0GmqiqbNm2iv7+fWCzGsmXLxKcpQRhG6enpLFy4kPz8fAKBACdOnODgwYNalzWmiaAZZCdPnqSlpYVIJMKCBQsoLCwUn6QEYZgVFxezbNky7HY7AwMD7N27l8bGRq3LGrNE0Awir9fLjh07iEQiWK1W5syZc9WrPAuCcPUkSWLKlCmsXLkSVVXp6upi06ZN9PT0aF3amDSqgiYWV/GG4vT7o3hDcWLxwVt5+XIcOnSIrq4ugsEga9asITMz84qfY3grFoTRS5ZlKisrWbRoEYFAgJaWFtavX08wGNS6tDFnxDQDxOIqrf1hajsC9HijBCNxQlGFUFQhElWIxtULfxRFRZYlDLqX/xgNMuZzfyxGHZlOA6XZVorSzQzGla3Ozk4OHz5MLBZj3LhxTJky5fUbAFRo6g1R2xmk2xMhGInjDsRYNTWNqYV2rU+1IIwaRqORuXPn0tnZyenTp6mrq2PHjh2sWrVK69LGlBETNA9ta+fwWS+93ijeYJxITCEcU4jEVGJxBeXcUEBVE6MCCS4EiCyBXidj1EuY9DJGg4zDrCPLZSTLaaQow8T4TAv5aWby00zo5CtLHlVV2bx5M263m2g0yspVqzCbX941M65AW3+Ilt4wjd1BzvaE6PJE6BqI4A3FiUQVur0RSrIsImgEYZClpqaydOlS+vv76e3t5ciRI2RmZlJZWal1aWPGiAma7dVu9td7MOkTowSjXsZh0ZHh0OEw67FbdNjNOpxmPSaDTDiq4AnF8IXi+IJxvKEY3lA8EVK+KO1AdVsAnQwpNj15qWbS7HqynEZKs62U51qZlGfFqH/zq4s1NTXU19cTi8WYO6eKstISonE43eqjpiNAbUeQLk+EPl+Utv4wbn+UuPJyEBr1iVGW6TJeSxCEK1dUVMSKFSt45pln8Hq97Ny5k7S0NAoLC7UubUyQ1MHcQnII/WptM95gnAynEbtZh9UkYzXqsBgTb9Ln/9dqlDHoZaIxhUBEIRiJE3zF/wYicQJhBV8ojtsfpbk3RH1XiNa+ELIsoZcl0u0GijLMjM+yMK/MycQ8G9muxE19RVFYv349x48fB6CsrIz29jZ6enqxmmRW3/Fu+qI29tZ5qO8M0tQbotcbJaYkLunlpZoozbZQmG4mxWbAZtZhO1dzZZGd3FTTtZwmQRBeh6qq7N27l2effRa9Xk9xcTG33347qampWpc26o2YoGntC2MxyjitevRXeGnrUmKKii8Yp3MgTGt/mObeEM29YZp7QpztCdLjjaKXJcZnWSjPtVI13oEt3sejf/p/NDY20tfXB4DVamVgwMOCRYvJnnYDStokajtD1HcGiSkK6Q4D4zISwVKYbqIw3UxemolslwmHWYdeJ1qfBWG4xGIxXnzxRXbs2IHZbGby5MncdtttYnmoITZigmY4dA5EaHeHaekNUdcZpLUvTGN3iPquIFlOPb0bvk/zie1MnTrtwqeg/v5+qqursdpdTLjvT7QNqIzLNDEu00J+2rnRS5qZ3FTThVGRIAjaGRgY4LHHHqO+vh6j0cjSpUtZunSp1mWNaiJoXkcoqtDWF6a5L8T2U/1s2bWfHb/9CLfcuBqn08n50ybLMh6PhxdeWsfc9/+S6xbOYcnktMTIJdWExSjuuwhCsmlqauKxxx7D7XbjdDq58cYbmTJlitZljVriXfB1mA0yJdkWlk5O5YPLsxmvnCQ/Nxun00k8HkdRFBRFIRaL4XQ6yM7OZpxykg8uy2LZlFRKsy0iZAQhSZ1vDjAajXi9XrZs2UJ7e7vWZY1a4p3wMmQ5DeQ7FawWM4qivObvFUXFajaR71DIEpfHBGFEqKysZNmyZSiKQldXF2vXrsXtdmtd1qgkguYy1HdHaIrm09bafG5+zss38M///7bWZppiedR3R7QuVxCEy7Ro0SIqKyuJRqPU19ezadMmwuGw1mWNOiJo3sSJFh9/3NzBmeh4PKqD6poaotEoer0evV5PNBrl1OlqPIqdM9Hx/GlLJ8ebfVqXLQjCZbr++usvbAty9OhR9u/fr3VJo45oBngD++oGeGhbB/vrvZj0kDKwn+oXf4FeJ2O1Wi80AqRnZJA68+0MpM4hHIOq8XbuXZLLvDKX1ocgCMJlaGxs5LHHHsPn82Gz2bj99tspLy8HYNeuXcydO/eatnUf63QPPvjgg1oXkYy2nOrn9xtaOd7iw6SXmV7s5K5F44n0t9DV3Y3NZiM3N5cpU6bwwMc+yvU33krXQJgeT4SW/jD1nUFcVgPjsyzXXowgCEMqJSUFo9FIzbkrFt3d3ZSXl2M2m9m1axeTJk0SQXMNxIjmEl443MMfNrXRNRDBpJeZV+7krlkuave/SG19E2azmZtuuonc3FxSUlIufN+Z9gAPbWtnd80AwUiiMeADy/O4eWaG1ockCMJleOSRRzh16hQAVVVVrF69GotFfFi8VmJE8wqKCk/s6+LnLzbjCcZIseq5aWYGH16ZT6Crlg2btl3Yl3zhwoWvmU2c7jAwc5yDSEylrT9Mny/KvnoPVpPMpDzbiNwALRZXkWSJkVe5IFy5/Px86urqCAaDtLa24nA4yM/PH5G/u8lEBM05cUXlyf3d/OCpBnSyTG6KiTvnZvGhlflEgx6eff5FIpEIKSkpvOtd73rdHzyLUcfcMheKCh3uMJ5gnE0n+0izG5iUZ0MeYT+w0biKTpYGZSsFQUh2FouFlJQUGhsbicVitLe3k5ubS1pamtaljWgiaEhsLbD2WB/ff7IRp0XPhFwrb1uQzd3zsonFYmzduo0TJ06g0+m4/vrrycvLe9PnnF5kx27S0+uNEogobD7VT36ambIcy4j6dKTXiZARxpb09HQMBgNnz54lEAjQ1dVFcXExNptN69JGLNHeDOw64+bXa1swG2XGZVr4+A2F3DQzA1WFjo4Ojhw5gtFoJDc3l5kzZ17Wc6rAmhnpfGJNISVZFixGHb9d38KO6gGtD1cQhDcxZ84cqqqq0Ov1tLW1sW7dOgYGxO/u1RrzI5ojZ738dn0bLX0hCtLMvG95HnNLE23Jfr+Pl156ifb2dsxmM3fffTdOp/Oynvf8ICDTaSTFZuBMe4COgQjNPSGK0s3XtB1AY3eQXTUD1HcG6fZGSbEZXrOXTbcnwrbTbuq7grT0hcl2GTHoXn5MW3+YXTUD1HUGsRh1OCwjZmsiQRgWpaWlnD17loGBATo6OpAkiYKCAgwGg9aljThjNmgUReVok4/fbWjlQIOX3BQjb1uQzU0zMs79vcKJEyfYvHnzheXE582bd8WvowLFGYmmgbrOAA1dIbq9EYoyzGQ5r3y5miNnvfzo6Ub+vLmd3bUDbD7ZRzwOUwvtGM5tOdDSG+I361v4xYvN7K4Z4PlDPViNOqYX2ZElCU8wxm/Wt/LHTa1sOdWPNxRnxjgHJoMY4ArCKxUWFlJbW0skEqGpqYnU1FRycnJef5t24ZLG7MdYTyjO0SYfoajCgnInJdkW7p6XfeHv3W43e/fuxWQy4XQ6uf3226/qdc6PbO6am0W7O8yzB3vYXTOAUSdz/4o8JuZd/nXfsz1Bfrm2mUBE4eAP5mHUyzx3qIfvPF6Pw6Lj3UtycfujPLStnS2n3Bz8wTx0ssTOM24++sfTTMq3sqA8hTPtAc52B9n+33MAuP+3J6lpDzBzvJNB2OpHEEaNtLQ0Vq1axfPPP39h8c3MzEzGjRundWkjypgNmhSrnncvyeXdS3IBGAjELvxdJBLh4MGDNDc3Y7VamT9//qBM1vroqgL6vFG2nnaz5VQ/ZqPMh1bmU5h+eZsu7TozQCyu8o23lFzYYnr5lFS6PQX0+aIANPeG2HrazX3X5aI7lxqzS5zcNTeLh7Z2sKA8BadFh82kY+upflQV7ObEpbMrzRh/KI7RIF8YSQnCaDR58mT6+/vZunUrHo+HtWvXcuedd5KZmal1aSOGGP+d47K+nLnd3d0cOnQIo9FIRkbGVV0yuxRZlvjo6kKqxjtxWvRsPtHP5pP9BCPxN/1eXyhGY3cIi1FHik3PsSYf++s9NPeGuW9pHp+6sQhFhT5fjGhMZeGEl5e/kSWJ2SUODjZ46PVGmJBr47opqXz6b2f47ENnWDollQm51ivuLjvbE8IXjF3ZNwnCCLRw4UKmTp2K0WikqamJTZs2ieaAKzBmRzSvx+PxsG3bNjweD06nkzVr1gzq82c4DbxveR6BSJwjZ72sP9ZHRYGNWePfuMnAF4rT748SCMd5/lAvf9rUSo8vSobdwIdW5XPv4lxUFfoDUQx66aKb+yoQial4Q3H6/DHSHUbumpPFXXOyrulYphSIdk9h7Ljlllvo6uqipaWFQ4cOkZqayqJFi7BarVqXlvTEiOYV4vE4dXV1HD16FJPJRFFREcXFxYP+OhNzrbx9QTbjsyycavWz7lgfPd433l7AF4rT0hfm+cM99Hoj7PjWHKp/spD/uq2YX65t4dHdneh10oUJoa9eWSixvQFiTowgXINbb72V1NRUzGYz27dv59SpU8RiYlT/ZkTQvILb7Wb//v0YDAZcLhd33nnnkL3WookpzC11kmo3sOuMmxPN/jd8vAroZInbZ2fy6ZuKLnx9yaRUbpiezn92d+ENxV4OEul1nkQQhKuWmZnJ0qVLcTgcAGJnzsskguaccDjM4cOHaWhowGKxMGPGDIzGod0tc+XUNMpzLHQORHnmYA+1HYHXfawsgdUok2I1XGgEADDpZdLtBvoDUQYCMfSyhKrCqzcClSSQZdCJIY0gXJPp06cze/ZsrFYr/f39rF27lu7ubq3LSmoiaM7p7e3l8OHDGI1G0tPTWbJkyZC/5sQ8GwsnpJDpNLC/3sPu2gEiMeWSj02zG8hNMRGOKcSVl4cmqqoSVxLrkZkNMhkOI3ElsajnK4WjKrkppquauyMIwsWuu+46Jk2ahNlspr6+nq1bt4ptoN+ACBrA7R5g+46d9PX14XQ6WbFixbC99qKJKZTlWInGFDaf7Odky6UvoaXaDJTmWOjxRC56TLc3SkN3kHEZZjIcRtJsejIcBp452HPhMZ5gjJeO9rJiaho2s9hTQxAGw+233052djZGo5H9+/ezf/9+AoHAtT/xKDTmgyYUibHr8Gk27zwAsoGMrGxKS0uH7fWLM8wsn5JKXqqJ480+DjR4iL7OqGbp5FRyUk38dn0L3Z4IDV1B/rixlV1nBnjf8nwACjPM3FqVwX92d7LheB+dAxGe2NvFiRbfhTlDgiAMjltvvZWMjAxMJhO7du2iurqaePzNpyuMNWO+vbmts4eXNu8mEI5htKWTN3UFKgzr/ivzyl3sqhmgpS/M8WY/Dd0hJuS+tmWyMN3Md95Wyv+90Ez5p3dg1MvMK3PxzBdmkHdu7TSjXubtC3IwG3S8/WfHMOolMhwGHvnktAuPEQRhcGRnZ7No0SI2btyI2+1m69atZGZmUlBQoHVpSWVM77DZ7/Hz6LOb2Ll1IzaHEzVtMubCOVQVW7lncU7iBA1T4mw40ccfNrTS54vxmZuLWFOZrvXpEQThMm3atIm9e/fi9XopKyvjxhtvJDs7+9qfeJQY05fOOrt72XfwMEajgaKCHFbfcCOhSITdtQN867F6mnpCDFcMzy1xMinPRp8/yp7aAdrd4Wt/UkEQhsXy5csvNAfU1NSwY8cO0RzwCmM2aFo7+3j8hS1E/f3kZGWw7LolLJlg531L80iz6enxRvnlumY2n+wblnocFj2LJ6VQkmXhZIufuo6g1qdIEIQrcMstt5CXl4der7/QHBAMit9jGKNBE43FOX2mjjOnTmA2GSnIy2bSlAri8RjjMs3cvzKfWSUO/KEY64/1XViwcqgVppvJTTFR1xlgX72HQFjcVBSEkUKn03HDDTeQm5uLwWBg7969nDp1SjQHMEaDpqmtk3Xb9iITY3xRPqvW3EwkklhGQlETkyBvmJ7OzTOz6PfH+PW6lmGpqyjdTJbTgE6WqO0IUNspPg0JwkiSn5/PHXfcQV5eHqFQiOeff54DBw6M+bAZc0Hj9gbYufcwrWfrSHE5mTSpnNTUdJRXTKVXAb1OYlqRjZnjHXR7Irx4pHfIazMbZcpyrKTZDNR1BmnsFkEjCCNNTk4OCxYsIC0tjXA4zK5duzh79qzWZWlqzAVNW3snu/cfwaCXGV9cwLKVNxCJvHZBS1UFk0Hm+unppNr0rD/ay6EGz5DXV5BuIifFSL8/Sm1HkFBEufYnFQRhWE2fPp2qqiocDgc9PT1s2bKFtrY2rcvSzJgKmrauPl7avBuvu4f83ByqqmYTi73+G7l67jLaTTMz8YTiPLqnk9b+oe0GG5dhITfVhKpChzs85K8nCMLQWLJkCdOmTcNoNFJXV8eOHTvo6xue5qJkM6aCpqG+gePHT2DU6yjIzWbKtOlvusS3JEF+mombZmbgDSlsGeIutLw0E/lpiYmVHe4I7SJoBGHEWrVq1YWVRo4ePcru3bvHZCfamAmaurNtrNu2j3g0SFnpeJavup7oZexsCYnl+avGO8hxGTnc4BuGUY2ZvFQTLX2h1yyOKQjCyGEwGFi6dCnjxo1DVVWOHDnC0aNHGWvz5MdE0PgDQQ4ePkJDXS0Oh4Py0hIys7JRlMvvBNHLEpPzbQRjypDfqxmXZaUow4wvFKe5N0Q4Ku7TCMJIlZ+fz5w5c8jIyMDv97Nv3z5qa2u1LmtYjYmgqW9qY9f+40goTCovTYxmolc2N0aWJaYW2jHpJPbVefAEh25XvYI0EzkpJlSg3R2huTek8RkUBOFaVFZWMmfOHOx2O52dnWzfvp3W1latyxo2oz5oOrr72LZrH91dHRTk51FZOQ3gqoaudrOOSfk2BgIxDjd6h2zDSrtZh80kI0vQ3h8WQSMIo8CiRYuoqqpClmUaGhrYsWMH/f39Wpc1LEZ90DSebebIsVPoJJXCglwqps244tHMebIkUVFgJxJT2F/vQVWGJmp0soTVlNg3xheO4wmO7clegjBaLF68mClTphAOhzlx4gQ7duy46vejkWTUB00kEsHd38ukieUsuW4p8fjV3++QpMR+L4UZFtr6ItR2Bods0U2bSYfZIBOOKuIejSCMEhaLhbe97W3cfvvtmM1mDhw4wD//+c9RP6FzVO1H093Zxk///DQbDjSQlp7GxHwnhkg/aampjB8/nty8gktOzrwSOlkixaqn0x2mfwjXQLOb9TisJgJRlagqdsUURqcnHnuUlpYWiseN58abbsZgMGhd0pCTJImFCxcSiUTYsGEDZ86cIT8/n+Li4guP6Whv5Z//eJi09AzmzpvP5MlTtC77moyKoOns7OQH3/8uG7bsoF+XR2/Mif7YIXa5q8lJd/LhBz7DyqtoALgUCXBa9CgqDARjQ7ZJmokQ7trtnD17lsOGqbxlxm2Yrc7hPrWCMKh+//vfE43FsOjhsec3capLJiqZcMRf4qtf+waf/MQD3Pvu92CxWLQudcjNmzeP/v5+9uzZc2EBTqvZSE1dPU9vPY6HdEwEsP3id0wuKeS73//BsO7+O5h0Dz744INaF3EtOjo6+MJnPsHfNzfin/AelMLlGHKmoS+Yi5I5nfbGUxj9Z5m3aBlOp/OiNc2uVo83Qm1ngOwUE1MKbEiDvDva448/xje/9Blajm3GFm7h1IEt/OfRRzGbzUyfPl2jMy0I1y4YDPLVL36WF5vSaU5ZRSijimhqBYGMOfRJObzwz1/iMsaZOr0So9GodblDymAw4HK56O7uxmAw0NpUz7d/8S9OW6/HnbmUWFoFofRKPPYKTp2pY/9zf2Dx0uWkpaVpXfoVG/FB8/9+/EP+vL4BueKdGLMnI+ktSHoTkt6Czp6F7CribM1xzOEO1qxZQSiiIssSknT1fzzBOCdbA6TajVSNdwzq8Tz++OP8+Mc/wWzUMW3KBPKy0snLySQYDLJr1y4sFosIG2HE+vjHPsqx+FTixTegc+YiGSxIBjOS3oreVUDElMHedY9y3ZypFI8bp3W5Q87hcFBVVUVN9Sl+8IdniUx4B3L2dGSj7dx5MSNb0pAchbS2d9B+fCN3veVurcu+YiP60llz01mOnaqB3NkYsyeDGgP1FSMWScKUPYVw/ywOHz3Bzl0HKCwqftNlZ96IqoISCqEE++nuDtLVpUeWr31Eo9Pp6O/v5/HHHycYDDJjxgxkWUZVVSRJoqSkhBMnTvDYY48xf/580tLSxvzS48LIYrNaaO4awFByDzpH5sW/qwCShLV0KYH23ezYvZfxpaVYrbZBuQqRrPR6PT093ew7eBi/tQjLuAVIahTUV/5uS+hdeVCynLrmRzh58gRTplRoXfqVHafWBVyL6tMnafUakBx5ictXr243VlWQZWRXAadaDvDbX/+a8ROnEY9d/b0aFYjFVaKBGC3NMo90WgflHo3BYKC2tpbq6mrS09PR6/UXAlFVVfR6PampqTQ2NvKLX/yCiRMnjom2SGH0MBl09Mm5SGbXpR+gqkg6PaROoLalh6effBIFaVQv16LX62k+28DW/afRpc5FknUQe3XDkgoSSOY0+uVsDh88IIJmOIVDISKKDlXSw+tMn5RQQNbjDyu0tLait6USu4aggUTXiCyBopNpZ3CuI+v1epqbmwmHwxgMhtf8cqmqisFgIBqN0tTUhN1uv6aRmSAMN4NeIvJmvy+qgqIzE44G6e7uIhQZ3T/jer2etrY2PL4gaqYZCeXS72QqIMlEMREMBrQu+8qPU+sCrkVWTi7pphC6mB8kHfDaAFElPVLEQ3m2ife88w4qps8gGhmckYAsJTZIGwwGg4GmpiZ+8Ytf4PF4KCoquujSmE6nw+fz4XK5eOc738n48ePFiEYYUSxmE49v+Aodb9SrqTNgCHWQ5cxi6bIVWG2j+9KZwWDgbGM9/YHH6enqQpUNwCUW0pUkJDWGS+2hoLBI67Kv2IgOmjlz55OX8mv8hw/jzJ6OZDCD8opPQLIeNezF13yYSVXp3H//B4jH44M6o3+wnkmSJKqqqjh8+DCPPPII3d3dZGdnE4vF0Ol09PT00NHRwc0338zdd99NLBYb1ZcUhNHHYDCgepqJdp7CVDQ/MQP6FT/Dks5IzNOOp/Egsz7+aZYtXz7qf84lSWLWrFk0NjbyzM+eJa3kenQWF2r8FR8iJRniMcLtxzFH+7j+hjVal33FRnTQALzr3nvZffjrnNr3MOlz341sciCpMZD1KCEvPXv+RoWxjnvv/TYgodPpIYnnPz7wwAN4vV4ee+w/OB12Ulwu3AMe3B4vt916K5/73OeAxJBbEEaaT3/zG3z6E18lFlewll6XuCejKqAzEPO00/fi97jjunIWLloEjJ2f8xvf9S5e3Lmfdet+TPrqzyPbMyEeBVlGjUXwVq/H3vAoD3z/q0jSyFvQRVJH+McFRVF4+snH+O8f/YYTHVGsedOJG1OQwm6CrUeZnm/km1/4KLfcdieyPDL+gfp6uvj1P57nn89spb+/l6pJ+bz7tutYtPg68vLytC5PEK6MqoIk4f/U5/GfqeUfy+bx/T8/hUdNJeooIS6ZMEe7CLUd586lk/n6lz/PjJmzBn1+WtI5d15i23bi+873OVRaxI8icV58dh/OcVVETVnIcT9Kz2nSpT6+/un7uO9994/I+UUjPmgAotEo1adPsXfPbv7+4iF2nOrG5nRx7y0L+NS9NzCuuDCZBzGX9OKRHn76+FG6+z28d8V4PnFHpdYlCcJV83/2i4QfeRRdJIKvuIjaL3ySaFYOcdmKKunQxQPEQ14mTprEuHHjx0zIRLfvxP+pz6OeqUUpyKPzrXdyaOY09mzbQ3uvF4fVxLQJRSxetJCp06aP2BUTRsW41GAwMHXadCZPnsTshSvo8EQJHV1H0cAu8o524zlqwFQ6F+vkxYnrnSOAL6QQN6eTnptBZk6u1uUIwlXxffJzEIkSefpZkGWiAx4y738f+W97e+IezVh0PmS27cD/mS8Qb2wCqwX19AnKOhcz5c67WDZnDsGAH73BSGZmFja7Xeuqr0nSBc21rB2m0xuZPqWM6QDT0hl4yUPXzieRdHpCZ48R6z6Lbc5t6Kyua3yloecPx/EHI6TaDBikET/oFMYg/2e+SORf/0GNxpBsVpTOTuy/+hnGD75P69K0cS5gkCSim7fh//yXiDc0QiSCYckKzA98CDkjA4D8gkKtqx1USRc0EvD84R5ePNxLrzeKcu7KnqKqZDiMfPbmIkqzrW/yLCrYsnDc+EmkjHF49z1FpPUUir+fmLsdx6J3YMhI7hZBfzhOXFGxGGUsxkuPwnp7e9myZQutra0XzamRZZlx48Zx++23a30Ywhjl/9yXCP39H0hmMwSDKB2d2H/1U8xjPGQiz79I5PmXiB87ngiZcATDiqXYfvpDdOOKL3rsaJJ0QQNwsMHLrho3t1dlkpNiAhKTvTYc7+cHTzXyiRsKmV78RmuMJf6RZIsTx8K3oc8owrvzXwRP70CJrCPu68cx7y7MZXO0PtRLCkUVguE4qgoZTgO5qaZLPs7r9XLkyBEkSWLJkiUXvh4MBjl9+jQPP/wwb3nLWzCbzVofkjBG+D/3JZAkQn/9O5LFgtLTg/3X/4dkNGK65+1al6eN85fK1m0k8PVvE6+uRnI4EiGzcjm2n/0oETKvGPGMNkkZNHpZYlymhfctyyM/7eU3yRnjHHz+oRqONPmYUmC/rMmSkt6Idcp1GNLz8aQX4t//NMHqncQ93di6G7HNuAHZklzL7/d4o/T7YyiqSl6KieKMSweFJElYLBYKCwtZuXLlRX9XWFjII488QmpqKjfddJPWhySMAf7/+gqhP/0VkJDsNpTePuw/+zHm975b69K0c34ks3YDgS9/PXE/xmJB6ezCePst2H7yPxeHzBvocIf50TNn6ffHkCRwWfR8cGU+k/NtWh/lm0rKoEGCuKISCF88I7gs20qqTY8/HCcaV9DrLr+XzJBdSuoNH0PvzMB38HnCzceI+3qJ9TQlRj3pyXNNtLYjwKlWP7G4SrbLSJr9jTeDutTimhUVFSxYsIBt27ZRVVVFdna21ocljGL+L36N0O//hORwoLoHUPv6sf+//8H8ofdrXZo2XjE6iby0PhEyZ5shFMR45+0Yr1+JfvYsdOPHvWnIhGMKLx7u5Ym9XRRlmCnONBNXVHo8Ub71WD1vX5DNHXOytD7iN5ScQaMmdrJ0Wi4OkkONXooyLEwrsmM2XHnDsmx14lx6H/r0Qnx7nyRYsxtf0Efc78Yx/y2Yxs3Q+sgBKM4wc9/SXKIxhcriq9uGQKfTMXHiRDZs2EBdXZ0IGmFIBL7+LQBCv/49ksuJOuDB9uMfgKpi/vAHrvj53qxFJ7lbeM4XeW4U8/hTxE6eJvLs88SbEiFjuGkNtu8+iFxcdNFj38iBeg+/WtfMgnIXX7ljPEZ94p6tLxTn24/X89+P1ZOdYmJBuevNKtNMUgaNLEs0dgf56r/qSLHpUVUw6CR2nBlg5jgHpdnWq76MKekN2GbcgD6jCP2uXHwHniVwaitxTzf2WTdjmbYC2aTdUFQFxmdZGJ9luehrV3q4kiRhs9lwOp34fD7NjkcYvfxf+jqhn/8aDIZEyHi92H74nWsaxUieAf61382h9ghxRUUB4nGV9NJs7p2bwngTyZ0250PmhZfw//d3UWrrQK9H9QcwveUObD/6PnJRwWXfj+nyRHj2YA8pVj1fuv3lkAGwm3V8bHUBOlnCbk7umYJJGTQAOknCZtLhMCdK1MkS4zLN7DzjZtcZN7dVZaK7hn1gTAWTMdz0SWR7KoGj6wg1HiHu6SbS3YBj3t3o07SZgS9d5tcuh8FgwGq1jv7Jb8Kw83/5G4R+/muktFTUgQFUvx/b9/4b80c+eG1P7HHz8NpmTttTuGmijXQd6EJeduw8y5HaAJ+9MZOFOYZre42h8MpLZc+/hP+LX0Xp6AQVTHffiW7aVIy33HRxyFyG9v4wZ3tCXD89HbPhtd2neWlmvnTbOJzWpH0rB5I0aBRFpTDDzJfvGHeh6wwSN8k/8oeTrD/WR9V4J0UZ19ZNJdtSSL3hYxgyCvEdeJ5QwwHie93Evf04F9yNsXBk7fnwatFoFL/fP6pXvxWGn/+rDxL82S+Q09JQQyGs3/4mAOaPffjan1yS0MsGFi4o5OsrXaQDEKNmay33Pd7Id+16fn5XFiXJ9AH+XHCEH30ctaub4O/+hNLRBf4AxttvwfrtbyLn5V702MvV643iC8Uoyrj0igAGnYQhyUMGkjRozjcDeINxclJe/nKGw8DsEidHzvpwB2IMykwYWYd9zh3oM8bh3f0o/kMvEji+kbinG8e8O7FMXIBkfLN5O8lHVVX8fj+hUIisrOS+USiMANEowZ//GtUfIPiTnyGnp6NGolgf/CqWBz4yqC8lSRCNxvHFIV0HKnrK52bx1mN9/L7By+GuLEqSZbGM85fKnnuRwNe/RfxsE3JqCgT8ia6yn/4QOTv7qluXA5E4A+c6UEey5AyaNxBTVJxWPSb94C4lYx4/A0NGATqLg8CpbYQaDhL3dBPtrMM2+zb0KTlaH/oVicfjnD59GrvdTllZmdblCCNZLIb/we8S/OFPkGxW5LQ0iMWxfu2Lgx4ylyIBGPWkmAzoemIMBBUgCZaSunA/Zi3+T/8XqseDZLWi9PZhuvM2bD/7EXJW1jVNwLQYdTiteuQRfvk7OYPmXNeZ7VU3uHq9UWrbg8wY5yA7ZfBXMNU5Mki740voM4oJHFlLuOUEnh2PEBvoxrHwrRhzJ2h9Zi7pUkupHzt2jF27drFs2TIcjqvrXBMENRwh+O3vE/zfnyJnZ6F6vKCC5cufx/LJjw3fLHZfmC5PDLPTSJZT45C5qHV5Hf5PfAbV50f1+zG9421IGelYPvXANYcMQLrdgMOip7UvdMm/jykqu84MEAjHWT09LWkDKSmDJqao1HUG+fXaZrJTTKgkJnGebPHhtOi5fnoaKUN4XdK5+J0Ys8bj2fMYwVPb8B9dS9zTjXPJuzAVTUUyDv4Kqt4YGPVguoLvUVWVQCDAqVOneOGFFy58PRQKUVtby8yZM1m2bNmQnSdh9FK9XsL/eQKltY3AD3+CnJEOOh2Wz3wcyWbD8qkHhi5kVNDrdVgvfM6MsnNHB39tlZm3OoVFGVqemHOjmCeeRo1GCXzlG4mQ8fkx3noTth99Dyk15aLHXovcVBMFaSbWHu3lnoU5GF/VENDeH+abj9YxvdjO9dPTNTwxbywpg2ZuqZOBQIy2/ggtfYltTRUVUm16PnljESVZQ79UtnnCfPRZ4+hT4gSrdxJqOEhsoBPn4nuwVa5O7OY5WEIe3McPoQ/0kJqTiyF/Mjpb6pt+m9PpZM6cObS1tVFfXw8kwkeWZaZMmcLNN9885OdJGH3UQJDA939E8Pv/i+RyJUJGr8fyuU8lRjEwhCMZCb1BofpkJ39QfGQYJIzdPTzeGCOjahwfnOUkRcuTc24Cpu9Tn0fp6UFOTUX1BzDevAb7b3+J5HQM6lIy2S4jN8/K4NuPNfCzF5v4zE3FF1ZE8Yfj/GFjK75QjPcsyUvqlWuSbj+aZGuRj3u6cb/0a4JndqKE/BgyirDNuhlb5Wp0zsxBeY1g7V4Gnv8Z4bNHsC14OymrP4zeJW7gC8NP9QcIfOcHL18q8/qQUlOwfPYTWD45hKOY81qbuecPLeyNmKjMMWGTVMJxlWmzi/ngQifZkrbvEZF1G/C990OgqqiRCITCGG+6Afuff4tkG5r5d6GowpP7uvjHjg5mlyS6beOKSoc7wsEGD2+dn807Fib3PeSkG9EkU8gA6JyZpL/1G7g3/J7giS1EOuuJbfwjsb5WHPPfgiG75JpfI9J8gqinB1WVMI+rFCEjDJ9XvGurPj+B7/6A4P/+DDkjHclqxXT3ncj5ecMTMucKCoVllqwq4ycrnKS+5m+1e4+IbtiE790fAFmXGMXceRuSXoftZ/87ZCEDYDbIvGNhDtOK7PzgyUaONycmYKfYDDz41lKmFSb/XjVJFzTJKmXlBzHmlOHb8wSh+gP49j5BbKAT19L3YMyfhKS/uuaESEctwdPbiTQdw1RciT4lWfo2hVHv3Lu20t1DbO9+Ynv3XQgZrBbMn/wYlo+f6yobxqXrJQkikRieOKS+ar6MFiETeXEtyDLeez+AZEjM8jdcvxLH738JhuGbPFpRYOehj0/V4AxcOxE0V8BasRxj7kT6X/olodp9hM7sJO7uwD7/bqxTlqCzX/nNOP/B5wmd2YMhp5zMd/0A07jKUbkfhZBkzoWM6vUR/J8fE/zx/0NKTTsXMlasn/0k5gc+PPxL16sq4YiCHIdkmGYc3bgZ77veB6EwWMyo/giGlctw/ushkJOgxXqEEEFzhfRpeWS+87v0P/dTgmd2Ee1uxP3SL4l1N2KfeyeGzOLLfi7fwefw7niEcPMJ8r/4lAgZYeidv/YkJTrLAt/8DsFf/AY5Lx81EEx0lH3mExeHzHCyWFk4LQ1DjhGbxr8G0c1b8dz1DiS7HRUw3rAK4gqOR/6mbWEjUNI1A4wk/kMv4Nv3JOGWU6ixCNaKpTiX3ocxdwKS7o0zPNxwkK6Hvkiobj+mgilkvvuHWCYt0vqQhDFA6ehEaWgk/MTTBH/6C+S0VKTMDPRTK9DPnzu0rctvIhmagaJbtoMEnlveklgsNBjEsGQRzif+pXFlI5cImmsU7WrE/eIvCTUeRgn7MeaW41zyLqwT5iFZXLQ0N9HW2kog4EOSZFLSM8iO9xF/4X8JNx4iFvJT8IUnsE5dIUYzwpBTvT78X/46oV/+Gik9A0mvR7LbsXzxs5g/eG7V5TH8cxjdsg3PTXeAJCOlpqCGQhgWzsf51KNalzaiiaAZJH2Pf5dg/UHiA13ozHaMVbdzJJ7NX59Yz3Mb99Lf0Q06HeWTS7nedpZbc/yUunSYMgvJePf/YpkwX+tDEEY51evD/4WvEPrzQ8jpiQUx5bRULF/6L8wfuG9MBwxAdOt2Bm64DTkjPdG6rKoY5s/F+fR/tC5txBNBM4i8e5/Av/8ZlN6z/GdfPV/dNEBg/K04p9yIMb0UNR4h2HYM34F/sFh3kK8sz2fRuz+HfdE7km47aWH0UNo7UAcGCP7sV4T+8jdklwspOxs5NwfTW25PjGTGeshs28HA6luQMzMgGkU/bw4oCs5nHtO6tFFBBM0gi7VXc/TP3+SmH6/FN+PTWMuWgySDEgMkJJ0BNR6l+6Vv8Z7SHr7ziz9SOKVK67KFUUoNBPA98GnCf/k7UmYGkqwDmxXbt76O6V3vOPegsRsysaPHUH1+BpavQc7KhFgM/exZImAGmejPG2T63In821NMrOxWzEXzEl9UYuf+VkWNR5B0Bpzz3stzzWZON3VoXbIwSqnBIL4Pf4LIvx9P7IeiqmCzYPvug4mQOf8Zc4yGTHTLNtyzFuK58fZzIRNHXyVCZiiI9uYhsHHjZuJZb0evM7z8y/wKajyCJXcanS/5aG9v17pcYRRSQyF87/8IkWeeR3I6kDIykK0WLJ96ANM73jqmRzGQaF0eWH0Lcm4OxGIQj6OfNQPnsyJkhoIImiHg9QxAvh1Jlkk0bL6WqsTB7iIUjpIcTZ3CaKB0dYMs4//4Z4g89yKSww4mE7ZvfR3j7bckHiRChoHVNyPn5ICqoptQDlYrzuce17q0UUsEzRAYN66YTn87aloJks7Ia8NGQo1HIOghxeVAhIwwKKJRfB96gMhzLyKnpyHZ7WA0YP/l/8N4843DP8s/mcTjKG3txOsbGVh1c2Ikoyjoq2aKrrJhIO7RDIE777wDfcce4sH+c7/Ur/zFlkCnx1+zicl5JgrSRbeZMAjicTx3vp3olm3I2ecWZdXrsP/25xeHzBgV2bCZvqIJeO58W+L8KOrLISP6oYacCJoh8P4PfJDieDWRMy8Q9/eAqiQ6zyQJVYkR7WtEPfZ33pLZRm7Ns0TPHk48RhCukNrXjxoK4bnlLUR37kayWJBSXEhOB/Y//gbjmutFyLy4Ds9NdyAX5CM5HMg52ehnVb4cMmP43AwX0d48FEJetv3ow3z0Z/+iJX05UtmNSK5iUGPQcwrl9H9412QdH56bTaY+guLIxDn/rVgrV6Ozp2ldvTBSqCoDK28ktnsfUorrwhum45G/YViy6MJjxuQbaSyG6vMT3bUHz213I+dkJy6VLZiH8z//GNvnRgMiaIaAe/0f8G/+I70drfyrOsQzLTraPQEkScesWVV8+KMf5ZY77iKy7a+4dz+BEhgAJKzTV+JcfA+GrPFaH4IwAgwsWUXsdDWSyQSKAqqK4/FHMCyYp3Vpmos88TSet7wTKT0NyWxOdJUtXojz338XAaMBETSDLNx0nI5fvZ9YXxuy2YY1r5TsTz0ElktvIRA6swv3xj8T7axFiYQwF1eSsvpDmMbP1PpQhCSken1IdhvuxSuJ19QiGQxIDgeqz4fz8UfQz52tdYmaC//nCbz3vPfCvRhUBcOSRTj+9ZAIGY2IoBk0Kmo0TMv3byXSVg2qgjGnlLzPPYbOmfGG3xn3dNP//M8Int6BqsTRp+biXHwPtsrrkYwWrQ/sZYqCGo+gKgqS3vimK1QLg889exHxuvoLOzqqkQiu9c+jnz4yN8QabOF/P4b33R9ITMCUZdDrMcypSiztL0JGMyJoBoOqEu1qoPNPnyDcdBzicYxZ48j74tPoHJd/z8W94Q/4dj+GGg2B3oht6goci+/BkFGo9RECEKo/SN+TPyDSXkPa7V/AMfeO5ArCUc49cz5KRyfo9Yk960MhUrasQ1cxWevStBWPg05H+JFH8b73Q4n1yiIRDDfegOMvv9O6OgHRdXbtVJXg6Z10/v6jxHpbQFWRrQ4y3vsTdPaUK3qqlJX3k3731zBkjoNYBN+BZ+h7/HuEGw9rfZQAKCEfSBKSTo8hs1iEzDDqr5yL0tkFOh0YDImQ2b5RhAwQ+uvD9JhS8H/2i8iZGajhMMZbbhIhk0RE0FwLVcW781F6/vMgaiyCGgmhd6ThWnk/psKpiZbmK2SZuIiMd34nsQmaJBNuPUnvkz/Af+gFrY+W+EAnajSEzpWNzpFx7U8ovLFYYo28/qmzUXt6QadDDQZxbXyB9J4WdJMmaF2h5kK/+xP+T3w2calMp0MNhTDdeRv2P/5a69KEVxAX2a+GqhL39+PZ9Bd8h19I/Levj+IfHkA226/56fVp+WS8/Vu41/8Bz7aHibu76H/xF4RbTuBcfA/61DxNDjtUf4C4fwBTcSWyyapJDWNJf0UVqtebGMXIMqrPT+rRvciFBVqXlhRCv/49/v/6ClJaamKOWjCI6e67sP/6Z1qXJryKCJorpMaj+PY+gW/v08QGEisvSyYrxd/bPbiXkiQ50X1WNBX3i78k2teKb98zRNpqSV3zMUzF04f1uGMDncT62lBjYYw5Jchm27C+/ljTP2EaaiCYCBlA9flIPX4AOV+bDxnJJvjzXxP46jcTu2D6/Jjf/x5sP/6B1mUJr0MEzeVSFXyHX8K/9ykinbUXvmarXIMxfyLoDUPyspaJC9Gn5TOw/ncETmwh2l5N7xPfx7X8vdgqbxi2ww/V7kMJ+xKtotmlSKZLB0248QiyLQVDZvGw1Tba9JdPQw2FEh1SioLqD5B66lBifa4xLvjDnxD4/o+QHA4klwvV68X84fux/c93tC5NeAMiaN6MqhA4vQP/vqcInT2SaJFUVUxF03AsuBvzhAVI55aXGSqGzGLS35JoEnBv+AMMdOJ+8VdEWk7jWHIPemfmkJ+GcNMxlJAf2WTDmFuOpDe+4hTFkSQJJDkx0hIdpFelr2RK4ufr3L0Z1e8n9cwx5NSUCyObsSzw/f8l+KOfJBYLjcdRBzyYP/kxbN/7b61LE96ECJrXo6qEGg/j2/sUweod576moHOk41jwVuzz7kSSdMPWly8ZLbhWfRBjYQV9z/yYuLcH38FniXbU4Fr9EUxFQzePQgn5iLSeQo0EMOVOuuj+TLjpOPqUnJfnCol5Clelb/zkCwEDiZBJqz2OlCaWJAIIfOv7BH/2CySbDbXfjeVLn8P6tS8lWpuFpCeC5hKUwAB9T/2IYO3exHwFJYZssGCbuQb7/LdgSMkBOfEJM9x4FFPx1XWYXQ3LxIVkpeTgXv87Aie3Em45Rd8T38O17L1YK68fktcM1R9ECQdAUTFkj0M2O1BCXiS9CVNhxbAc96ilqvSVVkA0mrihHYlANEpa7YnETe4xzv+VbxD+68NgMCBZrah9/Vi+9kWsX/6vxAPESG9EEEFzCUrYj//4BmSDGUN2Gdapy7BMXow+NR9Jp+OV14ZMRcMXMucZsktIv+srGPMm4H7xV8SA/rW/JtJRi3PZfcimwb1RH2k+jhoJghLHPGkJocZDmIqmIZsdw3rco0o0St+E6UgmI0QiiZAJhUirOwk6+cLM/zHp3Ax+/xe/RujPf0MyGhP7yfT2Ynvwa1i+8FmtKxSukAiaS5D0RiyTlmCfdROWiQtAks8tt3KJy0KyNlORZIsT59L7MGSX0/fU/xD39eE78EziUtrKD2EsGJyJfKqqEGo8ghIOYMgpw5A1DkN6cqxUMFKp4TD9k2dCJIp6fiQTDpNWcxzJOcbD+3zI/NdXCD/0j8SCodEoSk8vtv/5DpbPfUrrCoWrIJaguRRVvbAMjCQn/9A80lGL+6VfEzyzE9lkQ+/KxrX8vVinr77m5w7V7qXvqR8RaT9D7icfHtJ7QWOBGgjQP20OhEKJuTH+AJJBT+qZo0gul9blaXhiXl6HzP/ZLxL+579Bp0Pp7sH+0x9hev97ABLBI4w4YkRzKZI0opZXMeaUkX7Xl/HtfZL+tb8BVaV/7W+Idp/FufIDSNfQBuY7+DwxTxdxb89FnWbClVN9Ptwz50Pw5dbltIaTqNGoCBlJwvfRTxHdtv3C/CGlqxv7//0Y80fu17pC4RqJoBkldI4MnNfdiyG7hN7Hvkvc24N375NEOupwLX8/xrzyK37OwMmthGr2EOtuQpINoqPsKim9fQwsWo5ksaL6A4nzKEukHj+A5HKN7W7w8yHzkU8Seea5xH/rdCidXdh/9TPMH3yf1hUKg0AEzav0+aJ854kGnj/UQyz+8lVFWYKZ4xz8/RNTMeiSc4k4yWDGWrEMfVoB/S/8H6H6A4TqDxDrbcK14n6sU5df9nOpqoL7pV8RaatGjceQzfbEfCHhiijd3QwsWonq9aJ6fYkv6vWkHt4ztkcx8HLIfOjjRJ574cK9KrW3F/sff4P5/fdpXaEwSMQ9mlfp9kT48iO1hCJx/vutpYmJiEAkqvCDpxvxh+L84cNTcFmTO6Nj7g58e59kYOMfkC0udPY07FW34Fx2eb+8nX/4OP7DL6JEguiMFrI/8jusU5ZeaOsW3pzS1s7AijWobg/oZNQBD1J2Fqn7to/t1uVX3I/xffABIi+8lDhf7R04/v4nDMuuQ0pNRTKL+zGjRXK/W2pEJ0uk2AyUZl+8cOR7l+bxpX/W0DkQTvqg0afkvHwp7d8PEvN04d3zGNGeRpzXvecNt4vu/8unCBxdixoNIUkymff9BMvkJSJk3owKSBBvaMR71zvAZEJ1DwAgOR2kHNwF4bAIGUnC++4PoDSeJd7cApwLmYf+iOmdb9O6QmEIJPe7pYZUVUVV1QsjGlWFTKeBWFwlEhsZg0DZbMc6bQWG9EL6nvkx4ZaTBE/vJNJeS8qqD2GZvIRdu3by+KP/4tCRoyiKyoQ0PcsNjSxIi4DOgHPF+7FWLEPSDc1abqPGuTfQeF09ntvuRunuQTq3QZmUkY5ry1rkjDG+tcL5kHnvB4lu2pJYRiYYRB1w4/jnQ5je8VatKxSGiAia12HUyxdCBhIj/WcP9nDP4lzKc0fOEvmSrMdYMJn0t34T357H8Wx/GDUexb/ul3z/57/nuX3VtJhnEbauBknmaFsdmxoPsCJX4Wvvu4PUFe9Dtjq1Pozkdf4ykCQRr67B85Z3oHT3Iun1KH396CaU41r/3NgOmVecI+99HyS6fiPIMkpXN87H/olu0gR0JSVaVykMIRE0ryJJEuGownMHe9h22n3h66oKvb4oH7u+EJN+5N0UN2QU4lx2H4acUnoe/Ra/3dvCX0/p8VV9ASzpGIw2QELJnk530XKe3P1dCmr1fNbkYuQ0eg+zc2+gsSPH8H/8M6iqitLVDYqCXFCEa8cmiMUSm3KNVSqJgHnnfageL7GjxxIh09aO49GHMd5xq9YVCsNANAO8SrcnwlceqcPtj/KZm4sujGpicZX/7OnkxcO9PP7Z6VQUXvsGZ1pQYxEa9m1k/urbia36GfqcaaAqiTdNONd6qyfWfZrYpi+zc/Napk4b3r1vRoTzIXP4KN733I/S2opkNKJGoujKSnA+9ShyTrbWVSYF77vfT3TDZtRYHMlkRGlrx/mfhzHeebvWpQnDRIxoLkGWISfVyMIJKRd9PS/VyMkWP08f7BmxQaNIenY1egjnzMGUNQWU2MUPUFWIR9BnTiLgnMC2HbspLSvDYhk5lwuH3PmQOXAI7wc+gtLejmQ0ovT0op87G+ejD4uQOcf7ng8QXb8J9Hrw+VF6enA+9g8RMmOMCJrXoSgXNwMAZDmNZDgNdHsiWpd31eLxGCdPHENNnZBYuu11x7MquszJVNfWEw6HRdDARfcaYnv24fvwJ1Ba2iAWQzd9Gs7/90MkgwE5L/dCB9pY5n3P/UTXbgCDAaWjE+eT/0ZKcWFYOF/r0oRhJoLmCujkxGIu+WmX7u//2QtNzCtzMbvEiV6XnO8ykgQ6nQ69pLxByAAq6CUFnU53TUvYjBrnQia6eRvB//slam8f8ZYWiMXQV83C8dffIxfkX/TYscp77/sBiK7bAEYjSmcXzv/8A+PNa7QuTdDIyLurPUxe3XUGsOlkP/WdQW6sTH/N43/2QhM/fb6Jlr4QyXzTS5Z1zKisJN5xCPTm132cZLASbtlP5YwZmK1jeMl6eDlktm7H/9kvEN2wmfiZGohG0c+ZjeMvv0uEzCvvc41R3vvuJ/LSeiIvrUuETFc3zn8/hPH2W7QuTdCQGNG8igr0+2I8W91PXUfwwuUPVQVFVfn6XSVMzHv5jXf98T5+8WITkZiK2SCjl5P7TUan03Hd8hXkGz9He83zGMpvgng40RAAib119BYiNS+Sq7RRET6NUY0CY3AezSsulUU3bcX/uS8Sb2oGkwmlswvjDaux//bnyIUFY34UA+B934eIPPciksWC6najeH04//lXjHfcpnVpgsZE0LyKy6rn87cW8/YF2UTjyoWvS5JEpsPAiqkXb63b4Q6zZkYG5TlWvv1Y/Yh4r7H31/H5WSY+u+UhQsEBjOVr0NkyAIl4qJ9ozYtEDz/MZ5emkt66m/6nf4Rtzh2YxlVqXfrwORcckedeIPLE08Sra4ifbYZIGMPqVVg+9kHk3BzkokIRMoDvAx8h8vRzF3bBdPzjLyBLGG+9WevShCQg2puvUVt/mLxUE+GowprvH+JTNxZy86xMDEl6jyYeGKDzNx8iULuPjc1hHmk0s6k3HUznJmUGPSyvKubD776LJZFDxGt3gaRDnzUe54K3Ypt54+h/Uz0fMmvXE/jS14nX1CLZ7aheH4aVy7H//MeJgHnFY8cq34c/AbJM+JFHkew2VPcAjr/+HuNdoqtMeJkY0VyjvNREY0A4plzjMw2P3kf/m+CZXciqws1ldqo+9UNqOgfo6u5BVRUy0tOZNLmCqjlzUXoX4zk8Ae/2fxBpPcXA5r8QG+jEed29o3NJmldcKou8uJbAl79JvLkZzObEpbI7b8P+kx9ePIoZyyFz/8cIP/oY6HQQjaJ6vNj//FsRMsJriKAZI+L+AQbW/hrvrv8k7scYzLje/WPyZ91CFSR2FUW9aCsAOb0Q5+J3ondlMbDhD0R7mvDu/g9xby/22bdhzJug9WG9hvulXyVWnLY4cS59D5LhMlcAPhcc4f88QWzvfqLbdiRCJhDE+JbbMd56M/ppU5GLxaUyAN+HHiD878eQnA7UYBD7nxIb7pnuvlPr0oQkJIJmDAg3HcOz7R/49z+NqsSRdXrSbvs89lmv6ASSpEu2McsmG/bZt6FzZePd8S9C9fvxH3iWSEctjnl3YZu2MnlWdVYUvHseRwn5MWQW4Vj8zssLmvOXyp55nsC3v49SW4/kdCRC5rabsX3vW4kb/q947JgUi+H/4tcgHif8z0eRXE7UUAj7b36O6a13aV2dkMRE0IxywdM78Gx9iFD9QZRICNlkxTZ1Ba4V77+i57GUz0PvzMR38Dl8+58hXH8QJeAmPtCFY/5bkmLr67i/H0lvQDaaMeaUI11OAL4iZPxf+SZKRwdYEpfKTG+/G9uPvvdy6/JYvlQWjeJ74DOE/v5PJLMpMZKJRLD/8qciZIQ3JYJmkKgqeEMxonH13HwK7d+Q/EfW4tn+DyLtNYnLYjo9+vR8XCvvR9Ibr/j5DNkluJbehz4lh4EtfyPaUYdn5yPEfb3YZ9+OIWucpscbH+gENbHFg6l4Ouje4Mf7lfdjnnke/5e/gdLZier3Y77nHehnz8KwesXFITNGqeEI/k99jvDD/0ROS0V1u8Fkwv6zH2N6+91alyeMACJoBonZKPOZm4qpLHag03guTay/nVDNbjw7/020uxEUBRQFyWzDOvk6TONnXPVzy1YnjgVvRWdPx7vnMcJNx/DteZJo11nsc27DMmkxkk6bH6tI2+lza7XFMBVXIsmvU8f5+zH/+g9Kaxvhvz2M0tmF6vdjuusOrN/6emIZmVc8dqxSA0H8n/8Sob/9AznFBbKM7Sc/BIMe0zvF/jHC5RFBM0hMepl3Lc7RtIa4r49Q3X4CJzYTaTlBzN2FMbsE2+xbAAlUFXNJ1aB0jFmnrUCfno9v31MEjm0geHob8YFO4gOd2KpuQTYN/2oCwdr9qGocnSsLfXr+pQPi/KWyp58j8OB3iZ9tQk5xnQuZ27H9+AfI2Vlj91LZueNW3W6Cv/kDak8voT8/hJySAno9th98G9M9b7/osYLwZkTQjAJKyEeo/iDBk1sJNx0h2tmAbEvFNm0ltlk3YZm4cEhe15g3EdfK+9Gn5uHd/SjhtmqUbQ8nutLm3IE+LW/YzoEaDhBpPQ1KHPP4ma+9NPjqS2Wf/zLqwACSxYLS04PpbXdj+8n/JPaOGatvoOdDxuPB/+VvEPrDn5EcjsRIxmTE9t3/ToTMWA1h4aqJoBnB1FiEcOMRgmd2EarZQ6StGslkxTJxEdZpKzCNn4kho2hIa9DZ03AuuQedI3EpLdJ6Gu+uR4n2tWKffeugjaDeTKTtDErIi6oqmAorEkvpXDhRL18qU/1+gv/zE9QBD6rPh+nee5BzczB/+AMiZCQJ1T2A/8tfT4xisrJQBzyQkoLtW1/H9K63j93zI1wTETQjkBoNEemoI1S7j+DJLUTaqkGWMeZNxFQyC/usmzHmTxq+giQZ28wb0WcU4tvzOMHTOwkcXU+spwn7nDuwzbgB2Ty0+/eEGg8BiRZtY0HFyx1nF7rKnsP/pa+jdHYhp6ag+nwY77od2/e/hZSWetFjx5RXjE7Uvn78X/3muUtlLiSnA/PHP4KcmYHp3neOzfMjDAoRNCNQpKOO/md/kggYVUWfNQ5T3iSsU5djGj8L2azNasumwqnoXTno0/LxHXiWcMtJlICHuLcHx9w70bmyhuiVVUJ1+0FV0KfkoM8ofPkNUZKIPPsCvgc+A9EoksWM0teP6S13YP/lT5GczrF7KejccSttbUReXEf82AlCf/4bssuF5HRi/fqXxf0YYVCIoBmBYn0thM4exTx+JsbcCZhLZ2MqrEDn1HpvehWdMwPXsvvQubLw7voP0Y5avDv/TXygC/vcOzHmTxr0rrSYu5NoZ13i/kz5vAv3Z8L/eQJUFf9nvwjxeOJS2T3vQLJasD74tXMhw9h8Az0fMj29BB78LqE//AXJbkcyGpFSU7F+48vifowwaETQjECGzHGkrPoQlvJ5iTfuq5gTMzTOvRnJeuxVt2JIy8ez61FC9QfxHXyeaFcD9nl3Yq1YMYijLpVww2HUeAzJYMY6dSWSTk/k+Zfwf/wzqF4vUmpq4lLZbTdj+9mPkMyv2IdnrL1/viI4lO4eAl/5BqGH/omUkY4uLxfD6pXoJk+6OGQE4RqJoBlxVIx5EzHmTdS6kDdlGj+LtLRCvLsfxX90HeGzR4l7ey6MbnT2tGt/ESTCjYcSr1cwBVPxNCIvrsN73weRjAawWFAHPBhvuRHHX34PhlG4GOjlOhcc8cazxI8cI7J2fSJknA7kjAwsX/6vlydgipARBpHYJkAYQokVEtR4FP+B585NIG1ANtmwTl+Fc9E7El1x0tVv9Brtbab7b/9FLNhL+t1fx9AQwnvP+5Es5gs3/AEcv/sl6Mfw56rzl8q6uvF/4SuE//p3pPR0kGXkjAysD34V09veIgJGGBJj+DdPGHqJNyxJZ8A+NzGvxrPtH4RbTuLf/wzRznqcC9+GecKCq5rgqcajeHc8Qszfhb4+hHysA+/9n0ayWVH9AYxrrsfxp99qfRK098qQ+fyXCD/6BHJuLqrfj1xQkAiZt94lQkYYMmJEM8L5w3FOtvjpGAijnNsSRwVkCXJTTMwpdWpd4kXinm4Gtj5E8ORWYn2t6FKyccx/K/Y5t6OzpVzRc4Wbj9P9yFeQT/dieaYDJeRLrCjsD2BYtRznv/+u9eFq6xXBoXR34//0Fwg/8RSS3Y5uXDG6iRMw3ni9uB8jDDkRNCNcdXuAT/+1mmNNPqYWvjwqiMVV9DqZb9w1ngUTUpLqPUSNRfEdeAbvjkeI9jQjm23YKq/Hed296FMvbzUBJRyg75n/IfL8S1ie6UY1y6ihECgqhhVLcT76sNaHqa3z92PqG1A7uwj+6ndEHnsS7DbkrExs3/tvjLfdctFjBWGoiKAZ4c60B/jekw2UZVv42l0lF/3d1/5dx+YTfTzzhRmk2pLvJniwegcDG/5EtLcJNRLCVDQN59J3Yy6uRDJZX36gqhIIBjEY9BgMiQ67QO0u3N//LJanO1HNOtRQCOPK5ajxuAiZ85fKunvwffSTRB57EikzAwA5MwPb/3wX4y03ioARho24RzMKqEAoevFW0oqqctOMdLae6qffH03KoLFMXIQxpwz3hj8QqtlDqOEgse6zOJfcg73qFnyKjjOnT1JfX09P3wB2q4XyshLyM9OxPfoQlifbUa0G1HAEw3WLcTzyN60PSXvn5gUpvb34Pvgxohs2IefmoIZCyLk52H74PYw3rxEhIwwrETSjxKW2JuhwRyhIM2MzJckOmJeq25VN2u1fwLvncbw7/0Xc3YF7819oqjvN4x1Ofve3x2npcGNJLyAW9hPzdvCB5dP4+cb9hG0W4pEohkXzcT72T60PJTlIoPb143vfh4lu3goWC3JhAVJKCpZPflSEjKAJETQjnCRBXFFp7g2xr86DoqrIkkSPN8K/d3dy97wssl2XsZ2xlsegM+Bc+Hb0qfl41/6Krs52fvh/v+fvJ0w41nyZrFULUONRQCXuaeXZI3/jfU47qU4z+WUTcT7xL60PISnEG89CLI7/M18gunVbImTSUrF9/1sYVixLPEiEjKABETQjnCRJhCIKm2sGOHLWd+HrcUUlGlfJSzVx15wsZI03Y7sc1smL0WcUsfGHn+Pv9XbS7v4BelcBash94TE6WwaxBZ9l5d4fc8d4L/98/N9al50UVPcAvg8+QHTzFiRXChiNyKkp2H/zcwxLl4ilZARNiaAZ4RRFxW7W8eFV+Xz9Vc0Av9vQyg+eauCmGemsmpaudamXpSdmZH2giIzJKUgp41Cj/lcdcBwJsFa8l8cffxcejwenM7lauIeb6vHgufPtxI4cRU5LRy4uTOyE+aPvYViySIxiBM1d/ZRsIWmoQPhVzQAAt1VlMLvUydbTbq1LvGzegX4OHD1NMG06Ujz8Oo+S0JntZI+byoH9+7UuWTNKSytKZxeeW+8mdvRYYkFMlwP7L39Kyu4tImSEpCFGNKNYNKaiKCoW48vNAIqq0tIbJhxTkIBUm4F0R/J0pCmKSiQaR5J1vH7fvQqoxFSJuBLXumRNqH4/nrvvIXb4KHJaKpLBCDYrjn/9Hf3MSnGpTEgqImhGiUu9n3hDMYALEzljcZVDjV4e+NNp+v1RAFZMTeNH7yrHaUmOHwWHw8608kLqa2uwFs5CVWKXOlrUaAh87ZSWTdC65GGnBoIMLL2eeFMzcnoaxONgteB84l/op08Voxgh6YhLZ6NAXFFx+2O09Ydp6QvT2hfmdKufv2/vwKTXcWNl4v5MbWeA+397ki/fMY6any6i5qeLiCsqv9vQSiyeHPN20zMyWbNiAdbuXSjR0LkFN8+/aZ7bCTIWIlyzlhKXxPjcNNSRMqpRFeL+fuKebpSA++qeIhRiYNFy4s0tSDo9UmYGksuF65nHzoUMImSEpJMcH2OFq2bUy5j0Ms8c7OGZgz1A4gOtXidx3aQUHv7EVCAxmjnbHaQ028IN019uDHjPklx+/lIz/nAcl1X7HweLxcKaNTfy1LPr2Lr3/9BVfTgRNpIOVAU1FiLSvA/XqT/w+bdMoe0X7yP1ls9gHl+FZDRfewFDKB7w0PWnTxHtqMVcWkXW+39+2d+r9PYhWS245y1F7epC0unAYMD5n3+gKyt9+YEiY4QkJJagGcNUFf7vpSYON3j5v/dOxJEkl88A2o7t5j23r6Y6moW/9C6w50DEA51HsLRt5iefeAfLzK1EAn5UJYpz8T04r3s3stmudemvK+7rp/N3HyXu78M6cSHpb3vwsr5PDYdxz5iH0taB5LAn/uFkGde2DejGFWl9WILwppLnnUUYVqoKdZ0B/rWzkx+9qxy7OTl+FNRYlODJrcT/8QX+eN9cXqoPst1/mvqufaSnpbDyfUt5931/JjU1lcDRtfQ9/38QCeHZ8QjRrrOk3/VlZIszOS8fqQpKyAOShHS5O4xGo7inzkb1+18OGUkiZecm5MICrY9IEC5Lcry7CMPqfMi86+fHuWFGBosmpmhdEgBK0Itv39P0P/9TZEsKRlcW933po3xo8nWXfLx1+vXoM8fT/Y+vogQHCNXuoeN3HyH9zi8n2RbX56gKStCLbLYjGy8jaGIx+ibNgFAIZBnJbkf1+UnZuxU5L1froxGEyyaaAcaYuKJS2xng3l8cZ82MDL711pJrf9LBqGugi4H1v6f/xZ8jW5zo0wtIu+urmF4nZM4z5paT9+m/Y61YhmS0EB/oovP3D+DZ9g+UsP8yX314KGF/onFBkpDfYESjBgKJkCmflggZSQJFwbVjI2ktNSJkhBFHjGjGkLiisrt2gPf/+iTfuLuEdy3K0bokAKLdZ3G/9CuCp7cjG60YskvIuOe76J1Zl/X9ks5I+p1fxldciXvtr0CSGNj0Z6IdtaTd9nnkK9xQbUioKkrAi3Rubsvr3kuKRumfWIkaiSAZDOcWs4uTevIQUmoSHIcgXAUxohkjVBUau4N85q9n+NId43jnwmwiMYVITCEaV9GiI0SNxwhW76L3P98ieGYXktGKuWQWWe/5yWWHzCvZZ91E5rt+iGyyIumNBKt30PnnTxLtqOPC9qMaUVUFJTgAgCTrMOZPeu2DolH6xiW+LhmNYDQmQqb6iAgZYUQTXWdjRDiq8Ov1LXzn8Xp0ssQr/9VLsiw8/rlKclNNw9YdqwQ9+A++gGfnv4j7+pAtDmyV1+Na+UHka2xTVkJe+p76EaHavaixxMTUlNUfwj77tv/f3p3HV1Xf+R9/nXPuvuXehIQkBMIiEHYEUVSoslgVqIBVa1utTlvtMtp5dJn21848fj87004f46/to/1Np9OqtXZxxbqiSEVFQBaBEHaQJRBIIAu5uft2lt8fQRRXBJJzA5/nnwmc8zmHXN757iguby894cmsfIb4mieILXsALVRO9XefQFGPdygYJlgmnbUjQT3+u5+uE9m/A8VrT71CnE0SNKLX5VveIr7yr2R2rgIsVF+YwMULKLniS2d1tljyzWfoevUPWLk0lqnjGzOTyJxvoQUivf7MRipKx6P/Qr5lN+7aC6m47ecAWJks0SF14HC88+y6TqRxF4qnuI93EOJUyRiN6DX6scMk1iwivXMFZjqGZZk4SqspmfEP+MdfddbvF7h4Ac6KwXQs+jFmOkZmx3L0Y030u+nfcJQN6NVnN9MJso0NaP4wrurhAFiZDNEho8D5rr3mdIPIgV0obgkZce6QFo3ocXrXUVIbF5Pa+gpGrBUsC9UXwjd2JoGLF+Ls17OLDo14R3dX2oFNYOooTi/hq76Gf+LVKM6e/w/dKmRJbnye6Au/RguUEpn3HXxDp9I5pO6dkDG6t9EpPbj75OAR4hwgLRrRY4xEJ+ktL5NsWILe0dTdNWSBa8BoSmbcjueCKdAL0xC0UD/Kb/1PEqufILbir1jZJJ0v/JLcwc2EP/0NtFC/Hr2/lc+Q218PqgYuN85AFZ3DxpwUKKVNe8AyJWTEOUlaNOKsM1NdZHatIrH+WQqt+49vhJnHEa4iMGU+/olXowXtOYgts2cd0ed+jh5v6579VT2CsoU/wtGDrSq9q5Wjv/sqxBL4/tIMHhdkj5+1o2mU7tvePUYjxDlKgkacdV1Lf0v8jcdRHE4sPYcWKMM74jL8k+fhHjja7vIoHDtM9Lmfk2vaAoDmC1Ny1dfwjZ+NompnePWTWXqe9PZX6Pzzv+N/vL37iwrHdz51ULp3m4SMOOfJT7g466xCDjOXwlM5Ad+4mXjrpuEsqyma/cecZTWU3/Zz4qseJbF6EXqqk85n7yV3YDMlM798VrvSTCNLfsdmfA83g8MFWFjpDEpJCaW7N0vIiPOCtGjEWZfe8TpWPotn+MWo3uDxVkJxhMx7ZXatIrrkN+idzSgOF+6BY4jM+SeclcPO/OKAefgw0YsuRXF4wDRQQkEiWzZgZTIoJSG7H1+IXiFBI846y+g+FVPR+sZv6/nWfUSf754coDhcaCX9Cc++A9/Ymad9TWNfI7HZc1ACfqzOKJgmSiRCpGFt94p/Ic4jEjRCAGY6TmL1EyTWP4OZTaA4PfgnXkvJlV9CC5R+omsZe/YSmz1T568ZAAAYEElEQVQX8gVQFcgZqAP6E1q+GDVSbvejCtHrJGiEeJtpkt7xOrFXHiDf1ojq8eMeNJ7wVXfiqh55Spcwdu4mdu18yOVA0bACGtlbLiA4aT6heXfa/YRC2EI21RTibaqKb8yVlH32X/HUjsdMx8gdaODYU/9BeseKD/97x39XM7bvIDZ34TshE3KSvqkKgj68U06/G06Ivk5aNEJ8AKOrlcSaRSTrX8DMpdD8YfwTryE0/RZUX+jESZcnbNpM541fhGQSFAdm2EHmhmrwufHVXUHZwv9l9yMJYRsJGiE+hKXnyex4ndjyP5E/uhfNF8Y9eCLhGbfjHFBHV7STJx5/nI07dzJyz36+s24justHripA7IZh6HonjmAl/T7341PuehPiXNQ3pgWJPs2iWCc3fzTF4cI3bhZaqIKuZfeR2bMOpXEjbYkoLx5x8seVu4nqYdocA/EZw1lUBaHUTqaVa3xdS2KpQQIXfUZCRpz3pEUjesXmg0l+s7SJTQcSmMd/4izLwuPUuOGSCr47r9buEj9SoaOJ5JonyW5ZymPr9vEfDS5yw2/EPWASpuLEUhRMq4Aa3Udw72N8vqaLn9x9K9q130dxyHRmcX6TFo3oFV3pAq2xPDPGRLj50koM08KhKew+kuaJNa3kCiY/XDCkWDYPeB9nv0FE5t7FmoyH556+j1j1DEqGzUJRNTTLBCxQVCx3hEQ+x4qWh1ibLWeahIwQEjSidyiAz60xssrP5KHvrIivG+CnJZpj7Z4YXekCEX8R716suth2zOCNjhChKz/dveOBqb/zfctAUTWU8tEcSFzKc2t2MO1Gu4sWwn4yvVn0GssC3Ti5p9blUKkscZHXTXK6aXeJH+toWzsFRxgtUH5yyLzNNFHdAVK+oWzZvt3ucoUoChI0oldYdC+S97lP/pGLJgvsb8uycEoFlSXFf6qkefyAMtSP6AxQVCxFJZ8v2F2uEEVBus5Er3CoCp3JAvc+f5BH32jFwkJRFKKpAqqi8MMFQ+wu8ZSUlpaimBn0ZAea0919WNm7KUr3ztX5dsZNnGh3uUIUBQka0StMC7xujU/VhZlzYT8MEzQVWmN5nl7fzp9eb+HyESWUBop4jAaYeOFkLh22kq1Nq9BGL4RsjBOnhCoKqE7y0UOU7X+Wq+ffZHe5QhQF7Z577rnH7iLEue9Ae4aGAwmm1YW5+bJK6qr9jKjyM2lICKem8MZbXZQFnYyuCdhd6kcaUDMAS8+xZvmLZLIFtLKhKE4fqE4syyJ7cDWuzfdxY00X14/wYxw7hLN8MKpXjgQQ5y9p0Yhe8fahkgX9/cu2Bpd7CHodHOnK213mR7MsHA4nN157Jektf+e/n72PvduX4i+rwtLc5ONHqPLl+cats7m+Jo/SvJ7kppfQY20ELl6Id+Rldj+BELaQoBG2UxQFt0OlPPjOmpN4RufXS5rYfDBJWcDJXVcPZNwgO1s73Xub6bE2nFue47rKNDVX+GnUPHTVjsUoFKiuuJBx48YyccIEIvljtL/+MOlNS8jsWYcR78CItxOYMt/u1y1Er5OgEb3iw2admRas3t2FYVpMqysBusdt7n/1MI1tWeZc2I+Wziy/fOEgP735Aqojds1MUyi07qdr2f1kG+txJI/x6Vkz8c/5Dl3OUiw9TyQcQTtxNHM5kau+hrN0AKmGpeRadmEsfwi9s5ngZTehBc/ecdFCFDsJGtErLAsOd+b4zdJDrNrdhWl1d6elcgYep8Y3r6qhptSDYVrUN8Z5cdMx7v3icKaNDBNNFfj6A7t4ZkM737yqxpb6s3vWEVvxV3IHNoNl4Kmbjveau9DKh1D2IX/HUVZDyZW34aoaTnz14+QONJBY8yR611ECF83HM2yybf8eQvQmCRrRK0ZW+/j2nEE0d+Ywjm92ZgFOTWFCbYDpdZETf3Z4pY8fzh/M1OHdLRzLgmzBJOjRer1uM5sk1fASyXVPdR+G5vLirZtBePZXcZQN5OO2DFVcXnzjZqEGSkmseYL0lmWkt72G3nWUYHwh/guv7fVnEqK3yaaaomgdSxR4cHkzW5qSeJwqv/1KHU6tN9YYd4eHkYySXPc3khueR+86ihYoxTd+NqHpt+AI9+eT7ktdaD9AYu3fyGx7DT3ZiTNSTeDi+QSmzJdZaeKcJkEjilZnssCzG9tp6czhdqqMGuBn7oW9M7ZhxFqJr3qM1JaXMRLtOEoqCUyeR2DqZ9ECpZzu4QdmNklm++sk3nyK3KHtqC4vvglXEZh8He5BY3v3BQvRSyRoRJ/w+JqjPLi8hUfuHkdZDy7qNHMp8od3kmpYQmbnSoxkFGf5YAJTP0tg8jxUT4CzccJOdu/67q60nStBVfEMmURwygJ842f37osVohfIGI0oKnndZPPBJPtbM3zusv5A9xjN0P5e4mmDY4l8jwSNlU+TP7qfzM4VZN5aS6GtEcXpwTNiKoEL5+AbOxPF+faMtzM/y8BzwRS0YCmqP0Jmxwqy++sxuloxUlECF30GxenpzdcuRI+SoBFF59CxLPe9epgpF4QYWuHFMC1e2xZlUD8PleGemd6calhKsv4F8kf3YuWzOCuG4Bs3C/+YGTgrh9ITZ4Q6+w8jcs0/4qoYQmrzUvJH3qJr6f+gdzYTmDQXZ9XwHn7TQvQO6ToTRacjkefB11rY1ZJm1AAfsbTOwY4sd86qYXpduEfu2f6Xfya1+e84ygbiGTwR39iZeEddjuLonXU7md1vkFi9iOy+9ViGjm/UdAJT5uMdNb1X7i9ET5IWjSg6/YIubruimt8sPcS+1gx+t8ZXZgzosZABUJxeXDVjCEyag2/cLByRql59Zu/Iy9GC/YivLCHz1mrSu1ZROHYIIxXFP2kOiiofVdF3SYtGCCDV8BKqJ4R35FRQ7DumyUh0kli7iMzOlRTaDqA43QSnfZ7AhKtx9Bto92sS4rRI0AhRhNLbl5NY8yS5pi2YuTSBidcQmHIdngsutrs0IT4xCRohilTu0HbiKx8mu2cdZjaBq2oEoem34J94dffZN0L0ERI0QhQxI95O7LU/kt23ET3ajOL0UjLzy/jHzUQr6W93eUKcEgkaIYqdZZJq+DvJ9c+Qa96FmYkTvHgBgSkLcNeOt7s6IT6WBI0QfUTuQEN3V9r+esxMDHfteELTvoBvzExQ7ZvAIMTHkaAR4l2OduXZczRNLK3z9kfDssDlUBld42dQP3tX7OvRI8SW3U/2QANGrA3V46dk9p34x81C9Yftfn1CfCAJGiHe5eFVR/nZs40AVIfdvP3hiGd0LhsR5lvXDGRIhdfWGi29QHLj86TqX6TQug8zmyA49SYClyzAVTWcntjFQIgzIUEjxLs8uvooT73Zxt1XD+RTo945I2dXS4ofPLKXumofP735Ahyq/f+ZZ/dtJL7qYXIHt2CkoniHTSE0/Yt4Rl4qCzxFUZGOXSHewzAtElnjpK8NrfBy0dAg2YJJMqvbXSIAnmGTicz9Nt66y3FEqsk1beXY0z8jtf45zFzK7vKEOEGCRoj3UJTukz/fLZbR0U2L/iUuXI7i+dg4+w2kdMEPCF12E87+wzDzGY49+3+JvXw/+rFD3QNMQthM2tdCvIuiKGTzJjubU5SHXBimhcep8vctx+iIF7hj1gB8rt4/UvqjqC4foU/dirNyOIlVj5A7vJPYyr+Qb91LyaduxT1ssnSlCVvJT58Q7+JQFToSBf7rpUM89HoL0D20ns6bhH0OLh8ZZmJt0O4yP5B3xFQc4Upir/6B7L4NZPfXo3ccomTG7fgnzUVxuOwuUZynZDKAEO/y6Oqj/G1dG3ddXcOVo0tPfL09nufbf36LeEbnF7eOYHilz+5SP5SZSRB/41HSW1/BiLVhGTqhyz5HcNrnu4+hlu1rRC8rns5mIYqEaVmkcuZJXysPubjhkgqcDpWtTUm7S/xIqjdIePadRK65C1fNaBSnm67lD9Gx6MfkmraCaZz5TYT4BCRohDhFed1CU8DlfP/HxrK619q0xfN2l3mCd9R0Sq/7Lt7hl6AFSsnt20DHk/9Gsv5FCRvRqyRohHgPBfigZTLJrE6/oJNBZe/fHaA9kefe5w5w14O70M3i6Y12Vgyl9Lp/Jjh5HlqwDDNxjOjiX9K17H4sPS+z0kSvkKAR4j3yhkV7PE9bLE9LNEdHosCybZ28uj3KyCo/4wcFTvrzumGxfHuURWvbKA04i25dvuoPE772biLzvo2ragQoKrHXHqTtT98h37pPwkb0OJkMIMS7LK7v4FdLmthzJIVyPDIMyyLg1vjevFq+MnPA+/7Ohv1x/vh6C7phoesW9905Cq0Idg74IIXWRrqW3Ud233qsfAZHWQ0lV/6DnHEjepQEjRBn4GhXjuc2tpMtWPhcKit2RvnjN8YUbdAAGMkosdf+SGrTi2CaoGoELl5A5Jp/tLs0cY6SrjMhzsCWpiRt8QLzL+pHOtc3Bti1QITInLspnf99HBW1YBkkVj1K64PfQo+22F2eOAdJ0AhxmnY0p9h2KMWM0RGqwm7MPtQ5oGhO/BM+Tdn1/4Jn6EUoDie5Aw20PfQd0ttes7s8cY6RoBHiNCSyOmv3dGGaJpeNKCGa0inoFoYJuYJ55jfoJa7KCyhd+AP8k+eBomLE2+h89l66lv7W7tLEOUTGaIQ4DY1tGX76TCNPrm3FfXxdzdufpMtHhvn9HaOoCPWdLV+sfJbUlpdJrHoEvasVCwt37QTKb/53VG9xbrkj+g4JGiHOglTO4IFXm6lvTPDQN8b02Qlc+cO76HrlfrKNG8ECR0l/Sud9G8+IqXaXJvow6ToT4iwwDOtEi6YvjdW8l6umjrLrf0Rg0jywDIxEOx1/+wldy+63uzTRh0mLRgjxPlYuTaphCbHX/4yZSYCq4R40lorbfokcFS0+KQkaIcQHMw3yh7fTtewBsgc3o6gOtECEshv+N+7a8XZXJ/oQCRohxEcykp10Lbuf1MbFKA4XittP6NIbCF3xJbtLE32EBI0Q4mOZuRTJjYuJLXsALAPF4cJdM4by235hd2miD5CgEUKcEkvPkzu4ha5XHiDfvBNFc6H6QlTcci/OymF2lyeKmASNEOITsDBSXXS99N+kGpaiON2obj+hT91C8NIb7S5OFCkJGiHEJ2ZmEyTffIbo0t+hutwoLi/u2omUf+GndpcmipAEjRDitFiFLNl9G4i9+iD51n0oTg+aP0LF7b/EEam2uzxRRCRohBCnzzTQY210vfw70ttePTFuUzLrDgKT5thdnSgSEjRCiDNmZhIk1iwi9tqDoDlQPUG8Iy6l7Pof2V2aKAISNEKIs8LKZ8jseoPY8j9RONaE6vKilVRRcfsv0AKldpcnbCRBI4Q4ayyjQKGjifgrfyC96w0UTUMLlBK+5pv4xsy0uzxhEwkaIcRZZ6ZjxFc9SvyNR8Gy0AIRfGNnEZnzLbtLEzaQoBFC9AgzlyK97VXiKx5Gj7agegI4y2spv/XnqB6/3eWJXiRBI4ToMZaeJ9+ym9jyP5Pdtx5FUdAiVUSuvRvviEvtLk/0EgkaIUTPsiyMVJT4yodJvvk0ViGHFq4kcOG1lMy4HVSH3RWKHiZBI4ToFWYmQWrz34mv+CtGvB3VH8Y9YBRlN/0fVE/A7vJED5KgEUL0GquQI9dYT3zVY2QPNqAoKo7yWiLX3oVn6EV2lyd6iASNEKJ3WSZGrI34ykdIbnoRM5fC2W8QgSnzCU69AcXhsrtCcZZJ0AghbGGmYyTrXyCx8hH0RAeOkgo8QycTvvZuWeB5jpGgEULYxspnyOxeTWLdU+SatqFoGq7KCwhf/U3cgyfaXZ44SyRohBD2skwKrY3E1z5JeusyzHQcV9Vwgpd8Fv/kuce70ixAsbtScZokaIQQRcFIHCNZv5jEmicxuo7gKB2Id9Q0Sq64DS3Uz+7yxBmQoBFCFA0zlya9/TWS658lf3gnitONe+BYSmZ/FffAsXaXJ06TBI0QoqhYpkH+8A6Sbz5DeueK7q60mtGELrsJ37jZKA4n0pXWt8iSXCFEUVFUDfegcWihChyRapIbniXXtIWuTIxC+wGCU29AC5UjYdN3SItGCFG0zGyS9JZlJNc/R75lN4rHj2foZEquvA3XgDq7yxOnSIJGCFHULEMn11hPcsPzZN5ai5lN4K4dR+jyz+MbfQWoGtK6KW7SdSaEKGqK5sBzwcU4SgfgKKshVf8C2X0bMRKdFDoOEZg0t3tWmmWBImFTjKRFI4ToM8xsglT9EpIbnid/dA+qrwRf3XSCl9+Eq2qE3eWJDyFBI4ToUyyjQHb3GpIbnye7vx6rkMVdO4HQ9C/grZtmd3niA0jQCCH6pELrfpIbF5Pasgy9sxlnRW33uM24Wcf3SpNxm2IhQSOE6LPMTJzkxsUkNyym0LoX1R/BP/4qghcvxFk5zO7yxHESNEKIPs0yCqS3v969m8Ch7VhGAc/giQSnfxHviKl2lyeQoBFCnCPyzbtIbniO9M4V6NGjOMtqCF91J96R01B9IbvLO69J0AghzhlGKkpqw/MkN75Aob0R1RcmOGU+/slzcZYP7pF7diQKvLS5g8oSN9Pqwnic6knf39WSouFAgnEDA4wZeH4eWa2e+SWEEKI4aP4IwWlfoOTK23APGgdGgfjqx+la8htyjQ09cs+8bvLkuja+99e32LA/ftL34hmd/7ekid8vO0xzNGf367GNds8999xjdxFCCHG2KKqKq2o4zoohWPksRryDfMtuso31OEur0ULlxzfm7GYVclj5NIrTfVr3C3odTBlWwoubOmjuzHHh4CAlvu618A+taGH5ji7uvmYQ8yaV2/1qbCNBI4Q4JznC/XEPGouiKBjxNvTOZjK7V6NoThyhClRvECyLVMNLZPdvwlM7/rR3FigNOPF5NB5bfZSAx8FFw0Ks3RPj98uamT2ulJsvq8TtOH87kGQLGiHEOUsL9qNk5pfRQhUk1j6JfqyJ2Kt/oHBkD8Fpn0dRVWKv/AHLKOCqGo535KWnfa8bLunP6t0xnljbigK82NDBsEovt11RTdCj2f0qbCWTAYQQ54Xc/o3EVz9OrmkrZjqB6g3hLB9ErnlndyunrIbym3+Co6zmtO+x52ia7/7lLV6o7+DSESX86raRXDRUZrydv205IcR5xT10MpF53yUw+TNogVIKbftJbV2G4nABoHc0EX3x1xiJY6d9j+GVPiYN6R6juXJ0hBGVPrsfuyhI0AghzhuOcH9KZt+Bs/8QsAy0YL/unWoAFJXM3vXElj+EmUuf1vU3H0ywZk+M0oCT5Tu72NAYP63rnGskaIQQ5w3LNMg21lNoP4ijfHD3hADeGT1QNAfJ9c+S2vgClml8omuncga/erEJBfjRgsH4XSqPvnGUA+0Zux/bdhI0QojzhpWJk9qwGDOXwtIL8AFhojhcxJY/SK5x0ye69iNvHKX+QIJbplfx5RkD+Nfrh7LnSJqn32wjWzDtfnRbSdAIIc4bittPYMp1BCbNxVlei+oJYhk6mCbvbtlYhTzRl/4LPXrklK67fl+MB19r5pbpVSycUgHA9Lowcyf1Y/GmDl7eevrjPucCmXUmhDgv6Z3NpLe+SnrHcox0DDMVA1MHRQVFwTJ0vMMvoXTBD44fO/DB9rdl+MrvdtAv5OTeLwxnSIX3xPdiaZ07799BR6LAPTcMY3pd2O7HtoUs2BRCnJdUbwj34An4J89D80ew9DyWcbw7Tc+jqBqF9gNYpo574NgTs9Pe6/fLDnOwI8v3PlPL+NrgSWs+PU6VyrCbNW/F0A2L8bUBvK7zb02NtGiEEOK47IEGMltfIbu/HiObwMokMPMZyhZ8H/+Fc4mnMhimQUlJGE37+MCQo9e6SdAIIcR76NEWUltfIb35ZcxMAkvPc2TKHTyzooFUOsO8a6/i8ssvx+v1nvnNzgMSNEII8SEswyCz7RV2LX2YOT97muzga3D5gkS3LmbJUw8zY8aMU2rZnO9krzMhhPgQiqbhm/BpVq7ai3t4HGP817E8EUqBxUteZvKkSURKS8/4Puc6CRohhPgYQY8LzAJko2BZ5FJxgoFaVE1WiJwK6ToTQoiPkUqlmD17Fq1GOZbmxmrbwnNPL2L8+Al2l9YnSNAIIcQpSKfTPPH4YyQSCT57w41UV1fbXVKfIUEjhBCiR0kHoxBCiB4lQSOEEKJHSdAIIYToURI0QgghepQEjRBCiB4lQSOEEKJH/X/Wm0Umcgq4BgAAACV0RVh0ZGF0ZTpjcmVhdGUAMjAxOS0wNy0wOFQxMDoxMToxNCswMDowMGaZeA4AAAAldEVYdGRhdGU6bW9kaWZ5ADIwMTktMDctMDhUMTA6MTE6MTQrMDA6MDAXxMCyAAAAAElFTkSuQmCC)
8. From P, draw a line parallel to AC and meets the line AB at Q. Thus ΔBPQ is the required triangle.
Question 6.Draw a triangle ABC with side BC = 7 cm, ∠ B = 45°, ∠ A = 105°. Then, construct a triangle whose sides are
times the corresponding sides of Δ ABC.
Answer:Steps of construction:
1. Draw a line segment BC = 7 cm.
![](data:image/jpeg;base64,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)
2. Draw ∠ABC = 45° and ∠ACB = 30° i.e. ∠BAC = 105°.
![](data:image/jpeg;base64,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We obtain ΔABC.
3. Draw a ray BX making an acute angle with BC. Mark four points B1, B2, B3,B4 at equal distances.
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4. Through B3 draw B3C and through B4 draw B4C1 parallel to B3C.
Then draw A1C1 parallel to AC.
![](data:image/png;base64,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)
∴ A1BC1 is the required triangle.
Question 7.Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are
times the corresponding sides of the given triangle.
Answer:Steps of construction:
- Now in order to make a triangle, draw a line segment AB = 3 cm.
![](data:image/png;base64,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)
2. Make a right angle at point A and draw AC = 4 cm from this point.
![](data:image/png;base64,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)
3. Join points A and B to get the right triangle ABC.
![](data:image/png;base64,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)
4. Now, Dividing the base, draw a ray AX such at it forms an acute angle from AB.
![](data:image/png;base64,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)
5. Then, plot 5 points on AX such that:
AG = GH = HI = IJ = JK.
![](data:image/png;base64,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)
6. Join I to point line AB and Draw a line from K which is parallel to IB such that it meets AB at point M.
7. Draw MN || CB.
![](data:image/png;base64,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)
This is the required construction, thus forming AMN which have all the sides 5/3 times the sides of ABC
Triangle AMN is the required triangle.
Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts.
Answer:
Step 1: Draw line segment AB = 7.6 cm
Step 2: Draw a ray AC making an acute angle with line segment AB .
Step 3: Along AC, divide (5+8) 13 equals points
A1,A2,A3,……………….,A13 on AX such that
AA1=AA2=A2A3 and so on .
Step 4: Join BA13
Step 5: Through the point A5, draw a line parallel to BA13 (by making an angle equal to ∠AA13B) at A5 intersecting AB at point D.
C is the point dividing line segment AB of 7.6 cm in the required ratio of 5:8.
The lengths of AD and DB can be measured. It comes out to 2.9 cm and 4.7 cm respectively.
Justification
The construction can be justified by proving that
By construction, we have A5D∥A13B. By applying Basic proportionality theorem for
From the figure, it can be observed that AA5 and A5A13 contain 5 and 8 equal divisions of line segments respectively.
On comparing equations (1) and (2), we obtain
This justifies the construction.
Question 2.
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.
Answer:
Step 1: Draw a line segment AB of 5 cm.
Step 2: Taking A and B as Center, draw arcs of 6 cm and 5 cm radius respectively. Let these arcs intersect each other at point C. △ABC is the required triangle having length of sides as 5 cm , 6 cm , 7 cm respectively.
Step 3: Draw a ray AX making acute angle with line AB on the opposite side of vertex C.
Step 4: Locate 7 points, A1,A2,A3,A4, A5,A6,A7( as 7 is greater between 5 and 7), on line AX such that AA1=A1 A2=A2 A3=A3 A4=A4 A5=A5 A6=A6 A7
Step 5: Join BA5 and draw a line through A7 parallel to BA5 to intersect extended line segment AB at point B′.
Step 6: Draw a line through B′ parallel to BC intersecting the extended line segment AC at C′.△AB’C’ is the required triangle.
Justification
∆AB' C'~∆ABCby AAA Similarity Condition
And
Question 3.
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are of the corresponding sides of the first triangle.
Answer: 1. Now in order to make a triangle, draw a line segment AB = 5 cm.From point A, draw an arc at 6 cm. Draw an arc at 7 cm from point B intersecting the previous arc.
2. Join the point of intersection from A and B.
Hence, this gives the required triangle ABC
3. Dividing the base, draw a ray AX which is at an acute angle from AB
4. Plot seven points on AX such that:
AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7.
5. Join A5 to B.
6. Draw a line from point A7that is parallel to A5B and joins AB’ (AB extended to AB’).
7. Draw a line B’C’ || BC.
Hence, triangle AB’C’ is the required triangle.
Question 4.
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.
Answer:
△A′BC′ whose sides of the corresponding sides of can be drawn as follows.
Step 1 Draw a △ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = .
Step 2 Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
Step 3 Locate 4 points (as 4 is greater in 3 and 4), B1,B2,B3,B4 on line segment BX.
Step 4 Join B4C and draw a line through B3 , parallel to B4C intersecting BC at C′
Step 5 Draw a line through C' parallel to AC intersecting AB at A'.△A′BC′ is the required triangle.
Justification
∠A=60° (Common)
∠C=∠C'
By AA similarity condition
Also,
AB’=AB ,B’C’=
BC and AC’=
AC
Question 5.
Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ ABC = 60°. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC.
Answer:
Given in Δ ABC,
- Length of side BC = 6 cm.
- Length of side AB = 5 cm.
- ∠ ABC = 60°.
Steps of Construction:
- Draw a line segment BC of length 6 cm.
2. With B as center, draw a line which makes an angle of 60° with BC.
Construction of 60° angle at B:
a. With B as centre and with some convenient radius draw an arc which cuts the line BC at D.
b. With D as radius and with same radius (in step a), draw another arc which cuts the previous arc at E.
c. Join BE. The line BE makes an angle 60° with BC.
- Again with B as centre and with radius of 5 cm, draw an arc which intersects the line BE at point A.
4. Join AC. This is the required triangle.
- Now, from B, draw a ray BX which makes an acute angle on the opposite side of the vertex A.
6. With B as center, mark four points B1, B2, B3 and B4 on BX such that they are equidistant. i.e. BB1 = B1B2 = B2B3 = B3B4.
7. Join B4C and then draw a line from B3 parallel to B4C which meets the line BC at P.
8. From P, draw a line parallel to AC and meets the line AB at Q. Thus ΔBPQ is the required triangle.
Question 6.
Draw a triangle ABC with side BC = 7 cm, ∠ B = 45°, ∠ A = 105°. Then, construct a triangle whose sides are times the corresponding sides of Δ ABC.
Answer:
Steps of construction:
1. Draw a line segment BC = 7 cm.
2. Draw ∠ABC = 45° and ∠ACB = 30° i.e. ∠BAC = 105°.
We obtain ΔABC.
3. Draw a ray BX making an acute angle with BC. Mark four points B1, B2, B3,B4 at equal distances.
4. Through B3 draw B3C and through B4 draw B4C1 parallel to B3C.
Then draw A1C1 parallel to AC.
∴ A1BC1 is the required triangle.
Question 7.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are times the corresponding sides of the given triangle.
Answer:
Steps of construction:
- Now in order to make a triangle, draw a line segment AB = 3 cm.
2. Make a right angle at point A and draw AC = 4 cm from this point.
3. Join points A and B to get the right triangle ABC.
4. Now, Dividing the base, draw a ray AX such at it forms an acute angle from AB.
5. Then, plot 5 points on AX such that:
AG = GH = HI = IJ = JK.
6. Join I to point line AB and Draw a line from K which is parallel to IB such that it meets AB at point M.
7. Draw MN || CB.
This is the required construction, thus forming AMN which have all the sides 5/3 times the sides of ABC
Triangle AMN is the required triangle.
Exercise 11.2
Question 1.Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer:Step1: Draw circle of radius 6cm with center A, mark point C at 10 cm from center
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UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAJRS0UAJiloooAKKKKACiiigAooooAKKKKACiiigD/9k=)
Step 2: find perpendicular bisector of AC
![](data:image/jpeg;base64,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)
Step3: Take this point as center and draw a circle through A and C
![](data:image/jpeg;base64,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Step4:Mark the point where this circle intersects our circle and draw tangents through C
![](data:image/jpeg;base64,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)
Length of tangents = 8cm
AE is perpendicular to CE (tangent and radius relation)
In ΔACE
AC becomes hypotenuse
AC2 = CE2 + AE2
102 = CE2 + 62
CE2 = 100-36
CE2 = 64
CE = 8cm
Question 2.Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Answer:Steps of construction:
i. Draw two concentric circles with radii 4 cm and 6 cm respectively.
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)
ii. Now, draw the radius OP of the larger circle.
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)
iii. Construct a perpendicular bisector of OP intersecting OP at point O’.
iv. Considering O’P as radius, draw another circle.
v. From point P, draw tangents PQ and PR(can see in the figure)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAAE5CAAAAAC/1zOaAAAABGdBTUEAALGOfPtRkwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAACV1SURBVHhe7X3pbyNJll9m8r5vUqIoibpF3SpJpeqarumu7p7aq+Fd7w4WBow1sP+KPxj+7A/+ZsAwYGAN7Nro2RnP9nr6qOq6pZJEXaQkipIoUhTv+2ZmOqmDZx6RTNYUu1tZQH0QIyPe770XL9578SKSj0M/j4f/84AJQXdAf2qSvpPonUT/KBzwYgMdHqdLVfe/Z//TzwNoqdBhnN26vCC8nwnQTsO8cxg6z9EP3WOXWt3Os+UOaOd5+mF7vJPoh+V/50e/k2jnefphe7yT6Iflf+dHv5No53n6YXu8k+iH5X/nR7+TaOd5+mF7vJPoh+V/50e/k2jnefphe+xSicJwlS3lcgrTCDlzqUuBQtdA8XI27Aogvcs/MaA4htQkCUFo+uw0KtLZNAopZ4F2V6Y+fiQ3SgX8a7Bo2OVC9PN6tYI7SqKHrlJdNOHZEBj6eqQCuBzfdksnzJrOoOw2oOqVfCYcfIn0T/F8v8NtQ3qkI8K86qSrJMpXQ5A1nQgd/2PUZFjU189Xzoi7CmgFDU+l6it7iyoEw3/aQCGoZN+fTyTSv52cVXKWY62DrpMolHnjml55W/hsxxld6OvcJO06oPn1g+V7vBKkfGDZ/MOyrWP0dayjDmlZ8a3r4QwPwjGIN6jdX0vc5+4TXVPWZUDRXdf0LKGvV76uYgl24MuSzrCwy4Ce7k0s1+Ylf0m5jtwXdARpdwFNOtSL9RTxJpBN4UJHkHYVUMyVeHTtv+M31bXwWHJHNtUJkXYV0MtDS18TKHgh49D0dgBpNwEtHeTnW+qL+Mtf72jE3JF2E1C/Z1zVikg2v3Y6wd0b7CKg2AU0TQbIeu7qJWEASyF3EdBkeIg0+uTZnl0oOYu0i4CGYjPkrq2h78ikZSnAlubdAxSNSCisKzLs9P+EgKaTZiqu6wz+Ia75se6RaCoyQhWUCca3oj8doIm8ltLi9EDpn8wcLSfl1EKTauMFETeoXaO6RbSHuuqaZ7xI/1SA8iwiaqCIaT+t+4lIVGSlA6LEuE7SrlFdennxLDyU23mCHwlQwYyQY0LwRwIU4ThDuy45xs3g0L39I5EodwbcAeXOw+7q4U6i3SUP7tTcSZQ7D7urhzuJdpc8uFNzJ1HuPOyuHu4k2l3y4E7NH1ei+E3VJne6WffwvoDiZeIfjqLZIlR3YxKOy+QQgsA8Hrd0AWuY7yUexQooVozHSwkMS5aF0nqgEFrE+HIRXyqXyQQ8gYDz1hE44g5LtFgqFtKXiRIkkgvNQhWK8xsHIGQMo7lCzl9MicRGnYwnoMn9gaMAaNlBoGihlIwkLnk9GoOSzxciwoYq4zpaMLRcKpcKucJxFNZYVCKR8I8g2U4BRbNYxJMSqwYneWIRjz6RhSCCSvEQVioUy+GwU6Dpk4k7sHlPL9aOAMUyhZgPlvephCIReLIOERHJd10xj4a8ab1RIqqvnKo7PACgliBNOgC0mE74ckqrRsgCZJU0gUAGaYqF2FlRaVJx3TF7r8mxUvYiKBtS8ttBeUMYAVbZW457wwal5L3NVo4SzWeCAfWMnOMGELHK8SG5MXkm0svl4LoPorHVNpyA5mOhlGJK3ZkCTEQsUqT8fr1CyYkmKvQcOi1EAzHjnLgjlXpX5MESsTp55jPqVYTrxEpcAI3bBlpO+gP6e7K23yelDRbqVUnfsdYIQDnLJu0SGg1EZQuqjvMdggQ6dcQVi3XcALcHNOe/RMY17b3LKAmeUR3KFCPqznKxHWLx4EVqwNLOm4wgrxsI+yzOU7VJDtgcqFkb5Ga8QeVix45SkVOJm0fPj3Wmzhm6NmrqQ57skPk9LXZV1Diikp+cxAa4FzvedslWokXvpWKqQ/X8NCpXOSUxonYd9hs7xVKWQNNHBUtfZ60EJVxYr/B6k4Ocva7rAVgBxS+92FQnz1FRy/TK5xWNBI/jI5x39VkDLZ9dyifee+DYAN7Id+6NmDvh6bOQaO4oNdDBw2L0iwJ287P2/pErb+3AZAEHmjnMTmmAlqwONKplDvk2ka88zH2dAQYaO8E7esyRhBtltz/LHxlu/mVY7DkY5uwSggINHosnOQ9GL+rMC6eoENn7taW5mVno3p/k6iYBAg0cy8bf9+p5+vuPPhb4/vmrv29hqF5wuD/FESkYUO+RYYL7NGmUFB7LG+r7xPy6z3WQwfu9e6ZF8qrp/V0bNy8JBCh+7taOdxonBGPO8FTd8MkzQ8WBHl47bAUKSW2HezZOphAEaMBjGgNpx9LaavtPcrM1NS2mxZX1UnBVVd6S7pTZHIdTXCIJAAABp2m8AwtZCxuQMfHWu5WqA6LQutMaDImgY6QME9ucThuHecoM1H+oHn4fOAk4/Yh9ffkWqWRq79mfnrxz6ebJNUM87tiZbR8pI9DAodrWmTQfCf19vK2nq+qbH2YKe/91ryRTFCmWMenE3vZc20iZgCa8+tF2cRKnXcuJdDxxAwSGeGqZmrCddROw55799eqNkRE97HX09kniMQL57UHZBubIp5zOttdTBqDpM3l77heGRi59wWRBit1cZkPgw3lYVlgWGZVmswK5iTONq2uvPro1p0NDBLBCkdKoKWz7R9Ntsp0eaOGQZ2W/rmBo6MwdlsgRsQlWCOR18U4uVc6U0YuTFGwatuqu9oGV99eeL5nrsFW2nqge+ZjzcJJJCclfpn2r7EZGWMe9Rfe+j6+S96i1CinpbMvE4+FS1rnOG5qtJIUUq9vrS80nnqmQagYd0qG2ojY6oPhpfoTl5C8lth2QYcJg0FE7jDIZASt/GY4lfiOyzUp5smX7O7zFwaWA2lPwSXtYLthXzemAeqNWVukErOR+ndDbjGaAM5BiqxWKnAedG32zFvEivIdZwJJDyEDxQNSOi0QDNBLsMbDgHZ7c3S1aZvrB+a3TYd4L/w/Q/NSCcz83BoaUZ80cTctY0HXTlBpo3i21sJgN+e23ivHeQXYhDjIwkPKfbNlXrYLT8iSYWyIa23HMs7eQlEDxY/4wGI8rLCvsr/EWR9rJTSoU1svDr2VP+lzQGNjKoRg5uhhgIYJrkVICvcSHgaWDeZ5Hxqfb/biQcKDHcviNqcedvAdm4o3ZY7GJrfJSAY1e9gDHf1nHmvzJCJg4SOkTTg6d2A+HwttzQEhhS+KI9d2PFEBLZwLQPUrc8x26OgzMFXJJiCaN9kMoXFy5YRd9VYpgeO94Anxe0anuaWEEzDRAhYNn+k86cJmJ9tPh1/ZceRnIoCrN+2qWY5JLNJ7oAVxBY9/GPhrnEhBXJQwPqk3vXqYeAyE1Bx1aIDWvdk8KtOSR9INN9oun+cfDrC0gRd+qR4avvy9+UWExU0GVYGz3eJKV8pIC9ZUGgRQXdz2V/wXoXAbgHG/a9M3T5BMTBKMYsZ9GXBJI+ZK6/0hdHwow9k4GNBNWAtkW7Git/2MgTWMk46ZBQfQg+rvwI5jvz73DMAhWiQRioZjUnpuDLhOQNKg9I9wrsIJQVtpy2mbZTRS6bkvJdDoQSCQ1ez5DbzSxCaMQPxJWG9RGrVIhbwErGHL52KzcJBINxy0gayK6sb84015s2IoXjcei536ptn9Gjz57JnlwkP81kWSAS8VsIup9xxswGDSqJp7qQkdGFlt7rZSiASGQ5d5xLM6xMgfU4kwnwq6gaeQjiVBIOLFfCu07CdNthIISpc6ZyMFr7ZDV0BAzwsZzxyKI5lG5gP4k5Z0ldd3ibvtA5QK/DjyZi9M4f+RTsfhmyil/BTlOqkaCxxNDhv6JiO/4uG+8oVBFZz5Pg4fLLRItBSQgdvTsufljNraAkiH58+PzwU8U9cWhqieSby+OLXWqypPLLQsh+1P9sLUOmjXpmgde2lqAetNTAC/7Xxt+CTKRmQSOeT1H5i+b137lp9+ebMenG2YgTzpoim6+8o4NVEM0ueZkACDGJ1fdUkgEEG1Hf5B83gl7Gzk+Nv6ZtpVjMrMzf441u/hisy64/2xiolrUYAm5NQBSIfV1Q+gokxSIhM9r/NMO4MSPD/L3+0kVo6Tlowl7y1ahqN94uh+cvd3qV5i8KUBXtTkeReNCZoGW1y/+DMijoGdZ+mB/YoYiK1+yLLyWJNYW1c1diCZ61l5HJm/gmaMekq030mGb5mg4Osgs0EPHKivvi7zHyFrgkZXKbuPQ2NnBx7G1lRakkOqxe+1y8doXV0guxwBVqwlopMyc27pYGwSxVwwM8x6UP6fJcWLQx7mj+ydrC60KxhuTv36+el3q0Bc/G2eWTKVFI9B0WsuYdsrZhR9xd4hOtnpW6RdB8aPfOlaca3Mk3Oh9sr2Rt1XMkE4eGAYjprFVpDDJxB/MEfqCc/yJHx71UU3PKgHqmXXrw9d2hGSayO7v2qHKJa2I0R0Ay/I3AEVjCKMRCzknmLWbiVtnO2PE/c9Mz0J8z7CyuYWRyJQ3i+2KRogODJ6LNoBG44xGJmeXznP2/M42rVMMOK+Wx+Wv7I8X1+w5ko1oZBbb5BOGU6KIZIHKghokGkOZuIOfeL5gETKQy8y3obUxmoLKq/L5naOxpd3tMkkmjD+VXa9EHz0RH3ktQNPY9UBLWcbvjaQObKDbQZSKmdxQM6fArmvkbCe7vfIFxIWMtiqAZOnV20daSC8OjoJ4R/VAoymmHTnUFX8MZuSo519xS7AAmpbgLf/BuQzPC49zU60OlHTx2btPhDzFZRxk06me7HiG6Y3Y7ixXi4tuRqo73EzWCIJ6za5BA2TjufILrTNGe//F+gNEHwozkd20jpZzMoZNCNQNuhNEDcHhXmJjtef/yUW4DOPSd++WWpGaZ9eVM0ZXAGSS1kk0mTIyKHt8n3M5fdQ9AhA11Pikt/pjhMAs2M6be63KNJZwGI3ScAZgKtQBTaRm6IFiPnSMefWj1Ud0TUhxWzDVa0v/63CV+G1AaH/5oCWS4M2G154YIsFKkQfDUwc0jzAkJhK7s1yDlt3IA6BVr06kJs9kZdQeyZs3qy3DS2dfOkagCCug+ZyOQVyxlJWjyY27rS11x0yiePTV6VUtmWp1/eWKvrn1gP/IKMsCfAOnRnk6w7DBnXcNcjS5uB2eZsLV8rtB7p+8CsVUyxuvl1sM2eT5njEEsMDUAU1TX+R7NXra9SvgrWFyOL7LUfa6j0zbL6+DZNWDd6/vNzupqmGXGGIFNF+ih4HHxSDrFZ3EdgXsBUp8juo73002QHL/7evVZi912uvWxJgnaVWiaEFOP0Wz+2yLjpox+9Ij7fjJMn3wdv0Qrqy/mW3y+EQD+14AA1cFmkmr6BeXjOcv2iGzDu2h0AY8Q+to4c29DtyaMNHK9g4+2hg+jZ3sD+UZSasCzWYZDu/EeOBpcVI8sUgvIznVF+uuzIEH/k+4aquF9wQ7WONqLjPwYwnGnqtACyX6mDt/2sPYGb28XDBgeqe5G6n+siYxZJbnSDfWGY3vX+YZVaUGtEBvi/IXSwCOFt14IT5DJrVUhhABAqHN+7/8GVe4Fhwi06LD9aX6YMbQt50FBornpPSxcD6o4JZZ8BfptzPx/d+H+LKlx/hv8L9tJBsZXEvW/QUeE+2uLddlOWHrYQwYaLlAb7nwgJSj5noxeqco8E14ut+3htw/KDVTrUMbVXMA3nq1XGcxeox5jEkKt6pbyChpmxaDZgAbTsfXJELrLGD207+38Qv/9MI6SYinsdRcpImWGvStX7j3ZqVmUzSmQo5pXt0CRcv0Ge9i2MINaDyjo12+km7zBB8STR+cfNFSa470RpKNx2VNorVXD6sOKaIOAgMtleglWg7PAuWzKGUaLNMn3or5K0aqhJfqlj4Q01aq6VywemXtxS+qSBWXqRZ3v6mXW4mW8/Q4ilFuOKFQht7mimXBMmFKCyUSxUG0yRazql62v5y7rUEQZVJM1ugWaClHv6+blgJu5lANGMnShz7yEdfuvLCwVyDLi+himZZ+Nfe3t5GbIk9BOl77PZsswbCi2SuoSpTqWM11B3i8tQCGiYcNv5chhogAmT/715DJv/8R2aaIUNBiiSFIuri1Md9zZUJl4nS5am2efoXJMNuf9zeahNufcYjW6JbjHC9nSsFM+676v97Z2zP91SiZ5sC6eBVIjX+iBfubqfEKHgROZm5tOlYYetQb+eF//4fGXf9boAzFd1iS4w1DyRzjbof64VRBQi53WFAmAQqJFoQOuOLiw3gofgsUFg4sSoa8XyXIgQroP9iFlRXcjFGJx7w68ShvXEAUpRKZvyKcRfZLxNFWsahQrkoaDW4Yc0eGpva3EkXo/Z5ydIQb0AKfcZ+OZs4j8miO/JtqM7izNCkWCArVSQyj9i0tZv7bpqkCmO3CMwD5JzrrlE0BjkTaCYygdXFbfRNkVrWTXREgkcTtXzFk4ZcmXNrsFgAPTzEQqOnFMU4dkJ4+vBobsSL2d0s8FK1SgsnIqo+AgYIiamiH+iIlgamyBGAI8xyte1XY6AbyhSLq1weku3vp2sWusEhSA13r8r0CxY//x4WMZ36yQIx3/i8VKwgmVhh25L+pEyKM7qf+n5L0XRgm/hx5lhFXV0dkPE/m4L9XoLFvhH83mfrdP5t6IeT4eSX3RlAFM6OFYWf5v9zellJRTwgrr1cQtT48BMN4cNJcK41HhkivZX6vQF27f/cA6i3+w4tfQ6Wlz4wEpRViySmuxwAj/zn7H+slWvo+8pkRa41+rq6ahnHPgStc4wu55wMKtB1bgnrFFX/OojvGYUSqZ5MVlsPqBumpikbq188vZqTfMU0KQKCIor1azgp3RfwIUVQhyrExZ3VGtPJaKXt1RwPpU3IdDkz5GGOOqq9b8yxIp4IJQ1l7DDx9/oJwE5JJYu2WIvVpHzaYK23LUcoUZHHXOzkBFVVM/kg1emmNgxpmTTlUYJ8zGun9mm8uvcx9AUMCmPqMOgDsHE4Rc+ScgclxqJi/PRxP2Vc1uMnSKjnhg9VZQQDKrpr0fvnN10os+/kKIVERc+qVulu8JCefYwl7eZnQl3xKyLT/VQvTaKnnG8L0uk36NrJg2XKrP61sESnhMCh7SNrhcSmpRMMbyEIlh4JjGqZtulugfFJ3ojomIk4U2iFU//ln14GuRMSceqUeoEAeLV++kyxfzc0yqgKVqFBCX2mmzbc3x6pxLpwhiygBmRdTkzk752ua+9d/zyAa0LwuX0iSrKgjQ4C3obr1MHThMJuymwYO4BExicBcm70rN+mIkopxka6qrihHG4gJdCCFAjQCMnkCbQNF/aqWaLTsOuhfud3RzYsZiw5ugQoEaXqg+kieaRrQ6qGe772quWjnQUOWZiDl/fPxWilkDGJaRqsV2HxBhnZ9EZncWU5ARdJo218QxYPNNw3ldqJjtU3IbEAJLFGhLE4LlGd815bZrQlQnwy1q7uRcpMtym3GZ+r25nwh5otTqzkjIb1EIXmRI9D+E3ebQHF/b6OtiW3gS/X3E3jCzMpWdTh42SKtMyvQRwc41cdp5KE2Fxg0YG4AGnkruHITbp/cGdk+RpMxqAIVS7O0O2/SkYsxxhlPa2n69s+Zq2TIekBdS/VT0LcpvXYTbh+vT8tcXlEDKozp6fb1BObdPDegQ0fu9oD6i/UFM95N7Vyj6TmOA1y6VgUqk0XpM5pyXtwAUtNNKVWR2R8FPhxY1wvq7KlNSHTf3T/X6OD7IwqA74pU35HKL+iDdEnvUR/TtjL9Ijnu3XvUxjKKemuXJqOOw5Hm89bbuTEBs/WoAoXFaJm2uWT4O5ACYBokCk0gwRRkkLx+kTdWPaCN6OxYk1p5A2otgKLUtEAqTNAfBTaKAtx0F5p7vveQtUjx/Z7b/ancenKqpeJjnz+eADAeNaAySYgeh2zycIjZutEBUQ8eelmfJsmdzdwsLom3xdZ6fE9qmgfyle8aULkihtHqrqDfnuAGFBrzHPYyT6dGXh3Jb3gTfS6737LJWtgW2t7CzP5C3WlDvtjPkDLUDB3quW3wi+feOkBPtt7ARTd6r4FebMkbl8+rv7pLy+USY4xGNKyz1DJelH6SSke/AbtZiVp9+y9OjSCXAtR6OCr2Vzw23LdrtLUa/eDxQL8HrneTqMauA6qU+RmMjd5wzPXjJHM/7CnZpBPRN32jBO3o0c5I0/JZQZTegG1QGAJhXR1QuTJAP0khhe3VuJq12Wx4QTL7ameJKe1R94Y7sUDMFtThHJ0lyQNuRX4lLeaBkut1b8OKYIoeBtyjdKwA5vap+NG7sCaeBWYW+soyQSTqHadTZLcX7XlXjJA3D3Q3TD3ZahlJ1VYDTcqZl1agi1RokAxFD1RApFX6OCgQFw3nN6PTQyRacLw5ThQlRWEQzW04460QB8bptQruN60/4WZ4IXg2bRcyRaY3ycPsunkMSmwU5sguzLrc6ZuDoRKqBNoWqpcorIwlGCy1xPbMx/qITpN4RStv1peA9AJfgxcE8VfIElmNUmBNuEqYtUC+cgKa+WmYcfqwl2lJ6p9a1wM4XLQDy+6/+uEhiIfkcU33hd6K75ERdbYmf1jZ7r9EgTS38XoCuSLEVODLG7vYesjRHkHyB+u7MNMpawjKrRtm/W+1C2SJr6ON/qujrOmiHkhzm+5hUCejTIuvaurNGZiy0EhV8WDr2QLj2ZCd4mJ8w0RyQhaCju3WxSuAF3nGCxWu6WgUjiZ2yQQUGkps6dsIthphSxbRDXyMfsfVvTeBvu67RyIw9GRncP7q72U/UzHl7biNQIWyS8ZLn3i21PpDAC+a3j6IVzVbiUU6Hyn1SipzT5DdeJ07Opq4+bRFCGU6lk4OFNInfMQCTf9IJ19sr7Bwbsh7E9j4m+Upyuo/HvqsqPePk90a47Wj80M3MVCYD2LUWlUXkshCzPc39Mxs6CoOKLcHmdC9em6j+ohW8fmhSTzW25qkKni2kF/cLsOhWA9owUGzATXGvcznjcZS6yLAOy/pmKF/vLcWHCM9WM4/fF0yTrfaCyzoDIzW7gr1F0AF2nKRsEyZbDx5QUYpMpN6KwPI0zCJXL48sP5izEyiv/B57tH91mUl7D2FHl0XXVeeVAH86EbLktibPWd2fcSrW69XKecXE77a77zeL052jkYszV35DnW/XG2OPvFwwFWaG6izg5fFm4OlACO2AJWKwgAXPUoXXn7/uAMyhSQ2y+H+mVVjrPegz79af/JJU8ol54+cZaYn5HWzNhFUg1dStjo55swZwAUO0oVX360CTxAajsPKe6MHR4hJoa2maU5+kxu/vQ3x+s1iJOQP8SZGG76UjHnyVgBR3jRpBSpXhM0AiWr9x8++/RQ43KIjCFGvzEX29jQmpUwplcHQ+W9z/w5LV98oJuLJRNxv+EWvsHFNi4UtAHRSrKOVP1uyPmbDC0GaJ6++/wR8jtBClVh6MyfufYlKLFEWn519IUqlQ5VS5mIuW8hHIxnT1CfK5nUEvSDqOMEfEv9cbLiMgBgayUfPv/+EhfLQEsVTzk2VYv7w/haqs4S/PSk8hVDi05y5tEBjWjCKq99SqXVycUFyIw71GGSBiCnqB8qBSR49/8O9aY5xeJU0WCCQ9uX/9Xj0oRLNPc0PlFEI08uVcpi8+i13JmNlIsiAIuYTP1An4ofl7yK/ALd8jIqW/fbN6q8qEUNf5j4O4TSHcXBPdpnV3h5paKkJX6qBcvLSP9Fs4fcYAx5GgDcNPN/tfPQnVwMTUoRJC6lvu4r6we8nvXqHPIYe3D2zAbnt8ErPxtf3Jlnxlgo2av/H2F9+eh3QUJ+KuH67eC5gdmsaBiIHKjR5wmAZCmRQ9eIb31VSg+Pjf/429W+/ANuZwc6j1/Eo+EORFTFnLmSAi5T6yStHehrklmU6qvLOjT3Vr5fAcEKxkz62bhkFULjf6SW5uY2UVMEvrW//xbrClMGkZf7580By6R5gVgTKH0tG2M4WqjyXZOAYzPJW6B8wvHV+ZbsHZL/I8EY2PAX10AxoKgo9TjTcwwCkv5QJPV3SJwVWD8knMy+2jybn24IafXsG90rxGWCV8J9OAVNWZQJ15nIgdyYCnKZEb7ovXe+23WMzrKFe7p7lrWPh4jgwzrjD2IaPTQ2UN7jvYfGVSmR8yL2zvdHf8LE3JqUqn+zEYNOCwo4vqJna3v6e3+dPA9qs+i5pctEyq/t8AGg1ve5QMDHi3vT4ZAOzYIqFBpx7sHxw1hR+KQHHWTrMLrSzmNEl3Q1Fj4TVt4/44+OX+ydbO5LRcaa9lYL3xJkTKSaJmq/LNdUyMOnYacDWlidGu7tgLhyB7cnVdKSnJ3t+dnm0Wzb2WkzkRbTlWMDnTQpUBs0QcdkU7nbqAT86RYyCnx5OMu9lkM0CWqBwf94rYSz5bepWOjFR8HmCefsbVGnQyBUq+Kr07uq/ciIb90dRMV9sMQ9dVQ9hR07LDHgAFHb3WdmuoNf00e8XCcYdDhtbpMRptOFhKO25jJUyqWKxni6YL+LzelV6Y++Nrpa2fCPT4HYgZNcB3LRMatYYNsb41oMz0AvSG/uXTxF3VMfTmXTt8B0Rjyhk8vpajdJGeKq55I3G+obfqNv8KCeTRImb4McPXW3d/XZFr5p+0cisJxeBAt9r8Klt+Xzbmz4MEiXOWg07XaNsCmZA10OiBmO9XLfznfWjkErDp9bj1DvBPPtpdEsOI1BIO+ZyjgObf3CYxFHeAW3d/qPnv2mhcnn2M6pFOL6NzHLYa2cGChkQ59YMhyEosfMbsnjx2F/K8odbusfk7YMOSRtmsdYXAFBIZ9vbXOC898soa/WiDOp1nZPXgYe2dZNtz0/m5eWGOO3cwc4E0+01jEAYGvDj/1dZ9AlJjTAePDCNcTMUIBIlLsiadu5Ms/IG2cOGC4FTx8C/qXw4ofnBzk+M42CUUs8TMIpkNsfWFMOdl2A9UbYqa/9U9MKeu5ZbQ6KzdHZpHuKIk8EzqlElnXZt5QA/xNEeYoxvln6Z/L1ptPn1zEFqtBfce6IYHZhR4kmJKzPxXpaZa9IqZ5Lln/3DD5YrmdYcx+gBOsl03ToAa4GBQvwRiXN7DGRTBmBYkibWvyIQWv+m6VA9FjiQTXXC4oMDhSCzxPlqzszmDTaQ9TpCPfk2tCE4yXt8PVZOy8otCazI1swdO2Jj70l9b+zPdZbkBm30IDfKfGISiJ2sgEKyaYUjPUF/NyXQsECNSiGncL5Tc4UdUIhnVZ9sDHO9r5QZZmXvJe4Jmoc6orZXto550IYWsEbmdQVH9G3k4diMRGx2e88ksx0chi1QCBIOqU+2LP3vw8uvsYKXsEeG6itt2HCJtC17oBCsVfgP/CM9HdOqVsLSySC8wniHBCvwbQAlMrj9mjPH5YCOm5tNSWfCH/KNLLRFGTX29rqDFTazy97Ty/Jb2kAiSEZOClNDeHuEdRoo8eFp7b24Z1/do+2sAuOJcCjfOyCTMN6XC8S0ukbtM46v1yQOto0GgIPkoESh0Ug41z9IfF223MbtSfSjtA+0ItWVxMmhSiNivAcLBCkazWSCRWv/1Q1/TDUMIB02tuEClFiFder05UVeqdXQnvgHICsbj8QK4pEemiwgQC80TbgBJaSqUoxkzs+8Rg3zdSWUZJRS0WiGP2xEuFLzHoFWSoJUimHvRUrCVyqUbThM+Vi8hCXFkwY6lFhcUF/A2oZwO8JDRDo+mveeRYRSmUwJvktOTMVUtJhIZ3XDswj91lHx5QhoJQcFEzoClOgbkY6N5i8CYYmch0jVImZXAs2ns3m8GOWLx40kJY1N5OYur+665vB0CmglnyUdHc6nEsEiP4zDQplYJBaR9l4sFIr5ZE5QLmJy/aCCd42gGBLoqRNDMVaKQsaPzgGt9I5IpaYxLBZPJFC+CBFA/KJQ2Hj7ar4kLGMYjqaF8h6lrE5hS070MSVQNKzkGu53FmgFLMzT64nDyolCJp+M5YVQ6Wob+JrJuJj49JNUqpDIpM1mS6J0UzsJ2AWL6nly/e480OtxeDd7RVi2UDe5MOrPRCKqcq62891UwJpLjIDviv9xgd6OhshBK49k4qiawtjgp3LOGyLvS6Ls7aNC5hmgoKZ8xOpyXtKxuweoTHlSqlLT6OtG8yaumss6Z8ReUqBv8PTuKHllDebUAtfPUY7WPRKF9MoTM6lXEL3g/DlQ9llAUPm00U5lck2THVvH9mQM39EEGayLJMozn5yTAT33zVGZYxCEN226CChkGji2tmZR03Y9mxNLVNi7Cahw4PxoqYXQnSzwZ7/pBNxNQKGeIbv++rRbzTNyOuZZ1FxRQ+0qoPyR43e6Rk/KvT4EdgKHabp2FVBId+/Z5sf1S4z7tXGVa9xyzYLuAgqNBLfVdbcdHb4xsv0c9o/BGFX4vpx8Kbo9vYruveutfdePSTcZfu8yiUKSX/zwtEzUGhH6m948HFpuv8qxCXi3AYXUj168xaYRHD3bzN+zMeeeQAXddUAh9advX2XR5FNfz8MejgmxeiZ0H1BI9qD8PCJN37dyDs26GiheyPn8mDbPN3QUZ3ctL3gRzftOkiLLZ//Tm/hqeoLjV4kbpm9XqW58N5rADff0KlFB/oVj92hqSMryOOyPxAVE4T6bQlHxAWGJQTN6vLXfZzGKO4O1qySqvie8oQfHIL7ZMHrhcaoGjUpJSxYYdFGptesqoPxGagS9xpFkJPYu1f8R92KfrgLaIieeWm3J5ZI46DVUNILubqAE4YhMpmf6JhqIIncp0Ma8biccpC4FCiIjdm3ugLLjV6dbl+i/ENXGcF0q0aGWL7G3ga17XcAaZf++E4b2xwC0cwH3LdouVV2uitr6/h3QzvP0w/Z4J9EPy//Oj/6zkej/BzspHYNVpCpjAAAAAElFTkSuQmCC)
Justification: By applying Pythagoras theorem, we have;
PQ2 = OP2 – OQ2
= 62 – 42
= 36 – 16 = 20
Or, PQ = 2√5 cm
Question 3.Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Answer:Steps of construction:
i. At first draw a circle with radius 3 cm.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZQAAAFACAYAAACbaoqZAAAABGdBTUEAALGPC/xhBQAAAAFzUkdCAK7OHOkAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAZiS0dEAP8A/wD/oL2nkwAAAAlwSFlzAAASdAAAEnQB3mYfeAAAPd5JREFUeNrt3XlQnOeBLvqHpVmafRfN1oDYkUACsUjCCMlos2VJtmzjZTx2cpI6yUlOJudMam7NZO6dmVN1/7iZc1M5ub6pm5l4EsW2vMvajA0SEpKQQBICBC02sQqapdn3pYH7B+ZNtzYjCXh7eX5VFP01yPVgpH76e9/ve1+bhYWFBRDRfebm5jAzM4Pp6WnMzs4afZ6Zmbnv496vOzg4wNHREQ4ODkYf9z73oGMbGxvZPz7RY7OXHYBIprm5OfT39z/wY3x8HPPz85ibm3uiz7a2trCzs4OdnR1sbW3vO37UZw8PD3h7e8PHx0d8XnrMsiFTxUIhqzA0NCSKYmBgQDweHBzE1NSU+JienhaP9Xq9tLxLZypOTk7iY+l4qVjuLRoPDw/Z/5vJytlwyIsszcjICNra2tDS0gKtVov+/n5MTk4aFcfSx8zMzEP/OzY2Nt85PLX0nEKhuO9r9w6H3fv4QUNoS48fxbBcDEtHqVTC29sbKpUK4eHhCAsLg7u7u+xfB1kRFgqZvZGREXR0dKC1tRWtra3QarUYHR3F6OgoxsfHMTU1hUf9Nff09BTv9Jc+fH194e7u/p1DVI/62oOGwh72+N7nDIfe+vr6jIbhHsbGxgZOTk5wcXGBm5sb3NzcoFKpoFaroVarERwczIKhVcVCIbOzVCBLJdLe3o7x8XGMjo5iZGQEU1NT9/0ZR0fHB5aGj48PlEql0dDS0oeDg4O0n/FBZ1NTU1MYHR19YNH09/djfn7+vv+Ok5MT3N3d4ebmBhcXF4SGhopyYcHQSmOhkMkbGRlBZ2cn7t69i87OTjQ3N2NsbAxjY2MYHR3FxMTEfX9m6YVTrVbDx8cHHh4eDywNZ2dns5rk1uv1Dy2bgYEB9Pb2ijO13t7e+/68UqmEm5sbXF1d4erqioiICAQFBSEkJARBQUEsGHoqLBQySRMTE6ivr0djYyOqq6tFgYyPj2NsbOy+7w8ODoZarUZYWBhCQ0Ph5eUFNzc3uLu7w8nJCQqFQvaPtOqmp6cxMTEhhvt6e3tx9+5dUTB9fX33/RlXV1e4uLiIgtmwYQNiYmIQExMDJycn2T8SmRkWCpmMhYUFNDQ0oKGhARqNBlqtFkNDQxgaGrrve1UqFcLCwhASEoKQkBD4+/uLAnF1dYWtra3sH0e62dlZUS6jo6PQarW4e/cu2tvb0dbWhoGBgfv+jKenJ7y8vBAcHIz4+HjExMRg/fr1sn8UMhMsFJKuvb0dDQ0NqK+vR3NzMwYHBzE0NGR02a6/vz+Cg4MRGhoqxv+Xhm7c3Nxgb88r4L/L1NSUONNbuhLu7t27uHv3Ljo6OjA8PCy+V6FQiHKJjo5GdHQ0YmJiEBgYKPvHIBPGQiEpdDqdOBupq6sTJWI4oe7n54fo6GhERUUhOjpalIerqyscHR1l/whmb2l4bKlkampq0NjYiMbGRoyOjorvUyqVolwSEhIQGxuL6OhozrfQfVgotGbGxsZEiVRXV4sSMZwTcXNzE++IExMT4eXlBU9PT7i6usqOb/GWhhd1Oh00Go0oF8OSd3d3h5eXF/z9/cV8S3R0NOzs7GTHJxPAQqFV19nZicrKSlRVVaGnp0cUyRIHBwdxFpKQkAB/f394enrC09NTdnSrND8/L35HnZ2dqKurE+WydGmyra0tvLy84OXlhYiICGzYsAHJycm8W9/KsVBo1bS1taGyshJXr16FTqfDwMAA5ubmxNcjIyMRHR2N2NhYhIaGimEVTqibjtnZWXHm0tLSgoaGBjQ2NqKlpUV8j6OjI3x9fREaGoq0tDQkJyfDx8dHdnSSgIVCK665uRmVlZUoKyuDTqczulw1ODhYnI2sX79eDGnJvImQlmd6ehpDQ0MYHBzEnTt3xFlLR0cHAMDe3h5+fn4ICgpCRkYGkpOT4e/vLzs2rSEWCq2YhoYGVFZW4vr16+KMZElcXBySkpKQnJwszkScnZ1lR6YnNDExIc5cKisrUVlZibq6OgCLw2F+fn5Yt24dMjMzkZycDJVKJTsyrQEWCj212tpaVFZWory8HDqdDoODg+JrGzduFEXi5+fHeRELtDSRf/PmTVRVVaGmpgbA4tpifn5+8Pf3R2ZmJpKSkhAaGio7Lq0iFgo9serqalRWVqKiogI6nU7cx6BQKJCUlISkpCRs2LABfn5+cHNzkx2XVtnIyAh0Op04Y6mqqhJf8/X1hb+/P9LT05GcnIzw8HDZcWkVsFDosRm+YOh0OoyMjAAAXFxckJSUhE2bNiEmJgZ+fn5wcXGRHZfW2OjoKHQ6nXjDUVlZKS7G8PHxgZ+fH9LS0pCUlISoqCjZcWkFsVBo2VpaWlBaWoqysjL09vaK+0c8PT2RlJSE1NRUREREwM/Pj+tAEcbHx9Hb24vbt2+joqICVVVVmJ6eBgBxL0t2djYyMzN5VZiFYKHQdxoZGcHVq1dRVFQErVYrhrb8/f2RlJSEtLQ0BAcHw8/Pj1dr0X0mJyfR29uLhoYGlJeXo6qqSuzr4ufnh/Xr1yMnJwcZGRmyo9JTYqHQI924cQPFxcWoq6tDT08PgMW72TMzM5GVlYWAgAD4+fnxTmn6TlNTU9DpdGhqasKVK1dQWloKYPFyY5VKhbS0NGRkZCA6Olp2VHpCLBR6oKXhrdLSUmi1WjFUsWnTJmRnZyM+Ph4BAQFmtZcImYaZmRl0dXWhrKwMV69eRVNTEwCIHSZ37NiBzMxMeHt7y45Kj4mFQkZGRkZQWlqKc+fOGQ1vBQcHIzMzE9u2bUNQUBAXZ6SnNjIyAq1Wi3PnzuHq1avi4g5/f39ERkZyGMwMsVBIKC8vF8Nb3d3dABaX1cjMzMTu3bsRFBQELy8v2THJwvT09OD27dsoLi7GzZs3AXAYzFyxUOihw1sJCQnIyspCUlISgoKCZMckCzY9PQ2tVouSkhJcvXoVd+/eBcBhMHPDQrFiCwsLOH/+PAoKCtDZ2Wl09VZmZiaeeeYZBAUFQalUyo5KVmJwcBCdnZ0oLCzE1atXxdL5/v7+WL9+PXbv3o3NmzfLjkkPwW3urFRPTw+KiopQXFwMrVYLYHGpjMzMTOzatQvh4eHw9fWVHZOszNKS+F5eXoiJicHly5dRU1OD3t5eDAwMoLu7G729vcjJyeE8ngniGYoVunXrFk6fPo3a2lpxVhIVFYXMzEykp6dDpVLxMmCSbmJiAlqtFhcvXsSVK1fQ29sLAAgICEBmZiZyc3MREhIiOyYZYKFYkfn5eRQVFeGrr75CW1sbZmdnAQDbtm3DwYMHERQUxDW3yOT09/ejrq4Op0+fhkajAbA4txIZGYmDBw8iJSVFdkT6FgvFSnR1daGoqAgXL15EV1cXgMXtXHfu3Ml3emTyZmZm0NbWhlOnTuHChQsAFpfJDwsLw549e7Bz504u92MCWChWoKqqCqdOnUJ9fb0Y4oqIiMC+ffuQmprKdZTIbHR2duLcuXMoKioS++34+/sjIyMDubm5CAsLkx3RqrFQLJher0dRURHy8/PR1tYGvV4PAEhPT8eLL74ItVrNTa7I7AwODqKqqgpnzpxBfX09AMDV1RXh4eE4dOgQtmzZIjui1WKhWKilO5AvX74shriUSiV27tyJ3bt3Q61Wy45I9MSmp6fR0tKCEydOoKSkBMDiVYpLQ2A5OTm83F0CFooFqqysxMmTJ9HQ0CCWs1j6h5aeng4/Pz/ZEYlWRHt7O86ePYuioiKjpVvS0tL4xkkCFoqFOX/+PE6ePInW1laxqVFKSgoOHz6MyMhIbnhFFqe/vx/l5eXIz88XC026uLhArVbjtddew8aNG2VHtBosFAuSn5+PkydPorOzEwDg4OCAnJwc7Nu3D+Hh4VwZmCzW5OQkWlpacPz4cZSVlYnn169fj1dffRXp6emyI1oFFoqF+Pzzz/H111+LPUv8/Pywf/9+bNu2DevWrZMdj2hNtLa2oqCgAF9//bW4CEWtVuPw4cPIycmRHc/isVDM3OzsLD7++GOcPXtWXEYZFBSEV155BampqbxRkayOTqdDQUEBTp8+LXaGDAoKwoEDB7B//37Z8SwaC8WMjY6O4sMPP8TFixcxOjoKAAgPD8df/dVfITExkTd6kdUaHBxEcXExTpw4gf7+fgCLS7bs3bsXL730kux4FouFYqZ0Oh3++Mc/4saNG5icnAQAxMTE4O2330ZsbCzX4iKrNzo6ioqKCnz44YdiAVRvb288++yzePPNN2XHs0gsFDPU3t6OP/zhD6iurhbjxImJiXjrrbcQGxsrOx6RyZiZmUFtbS3ee+89tLS0AFhcByw7Oxs/+MEPeKHKCmOhmJn6+nocPXoU1dXV4rnNmzfj9ddf5652RA+h0Whw9OhR1NbWAgCcnJywdetW/PCHP+QNkCuIhWJGbt26hQ8++ED8owAWVwo+cuQIIiMjZccjMml1dXU4duwYKioqACxuM5ySkoIf/ehH3AlyhbBQzERZWRk++eQTNDY2iuf279+P/fv3IzQ0VHY8IrPQ1NSEU6dOoaioSDyXkpKCH/zgB1CpVLLjmT0WihkoLy/Hn/70J7S2torn8vLy8Oyzz8Lf3192PCKz0tnZibNnz+Lzzz8XzyUlJeFnP/sZdyl9SiwUE9fY2Ih3330Xzc3N4rkf/vCHyMrKgoeHh+x4RGZpYGAAly9fxr//+7+L51JSUvC3f/u3XJ7oKbBQTFhXVxd+85vf4Pbt2+K5X/ziF9iyZQvvMSF6SpOTk7hx4wZ+9atfiecyMjLwi1/8AgqFQnY8s2QrOwA9WF9fH373u98ZlclPfvITZGVlsUyIVoCzszOysrLwk5/8RDxXWlqKP/zhD7KjmS0WigkaGRnBu+++i8rKSvHcO++8w7WIiFZBTk4O3nnnHXFcVFSEjz/+WHYss8RCMTFTU1N47733UF5eLp7Ly8vDnj17eBpOtAoUCgX27NmDvLw8AIv/Bk+fPo2vvvpKdjSzw0IxIXNzc/j4449x+fJl8dzBgwfx3HPP8eYrolWkVCrx3HPP4eDBgwCA4eFhHD9+HMXFxbKjmRUWigk5ffo0CgsLMTMzAwDIzc3FwYMHeTUX0Rrw8PDAwYMHkZubCwDo6enBJ598gqtXr8qOZjZYKCbim2++wcmTJ8U2ptu3b8eRI0d4XTzRGvL19cWRI0ewfft2AMDdu3dx7NgxoyFoejgWigk4f/48Pv/8c+h0OgCL18Pn5eUhMDBQdjQiqxMYGIi8vDykpKQAWNy06/3338etW7dkRzN5LBTJLl++jE8++QTd3d0AgLi4OLz55ptcToVIotDQULz55puIi4sDsLhki+HikvRgLBSJbt26hY8++kjsAa9Wq/Hmm29yoUciExAZGYk333wTarUaANDQ0IAPPvhA/Hul+7FQJOnq6sKxY8fQ3t4OAPD398err76KhIQE2dGI6FsJCQl49dVXxZp5Go0GJ0+exNTUlOxoJomFIoFer8epU6dQV1cHAHBwcMDBgweRmpoKW1v+SohMha2tLVJTU/HCCy9AoVBgbm4OJSUlOHfunOxoJomvXhKcP38ely5dwtzcHABg586dyM7OhqOjo+xoRHQPR0dHZGdnY8eOHQAWV7I4ceIEbty4ITuayWGhrLHq6mp88cUXGB4eBgBs2rQJhw4dgru7u+xoRPQQHh4eePHFF5GYmAgA6O7uxgcffGC0pQSxUNZUd3c3Pv74YzGpFxISgtdff50b+xCZgaCgILzyyitiPqWpqQnHjx/H6Oio7Ggmg4WyRubn53HmzBmxerBSqcShQ4e4DzyRGUlISMD+/fthY2MDYHEn1YKCAtmxTAYLZY0UFxejuLgYer0eALBr1y5kZmaKv5hEZPoUCgVycnKQlZUFAJiYmEB+fj5KS0tlRzMJLJQ1oNFo8Omnn2JoaAgAkJqaigMHDsDV1VV2NCJ6TF5eXnj11VfFTY+9vb04duwYGhsbZUeTjoWyynp7e/HJJ5+go6MDwOLNi2+88QbWrVsnOxoRPaGQkBAcOXIEPj4+AICWlhZ89tlnGBgYkB1NKhbKKlpYWEB+fj5qamoAAG5ubjh8+DDvhCeyABs3bsTevXvFcUVFBfLz82XHkoqFsoouXbqE8+fPY3Z2FsDicvRpaWmyYxHRCnB0dMSzzz6LrVu3AljcmOvs2bO4dOmS7GjSsFBWSVtbGz755BNxCpyRkYH9+/fDxcVFdjQiWiE+Pj7Iy8tDVFQUAKC/vx8ff/yxWFLJ2rBQVsk333wj/lJFRkbitddeE9evE5HlUKvVePHFF+Hm5gYAaG9vx9mzZ2XHkoKFsgoqKipQUlIijvfu3Yvw8HDZsYholWzevFlsygUsDndXV1fLjrXmWCgrbGhoCMePH8fg4CCAxUuEMzIyZMciolXk7OyMAwcOiH2M+vv7cerUKUxOTsqOtqZYKCvs0qVL4m54Ly8vvPjii9wTnsgKBAcHY/fu3eL41q1bVnfDIwtlBTU3N+PMmTOYmZkBADzzzDOIiYmRHYuI1sj27duRlJQEYPEu+uPHj4vdWK0BC2WFLCws4Ouvv4ZWqwUAREREYN++fVAoFLKjEdEa8fb2xsGDB8UEfVtbG86fPy871pphoayQGzdu4OrVq+J47969XEWYyAolJiZi27ZtABbfaJ47dw719fWyY60JFsoK6O/vx+effy72OElJSeFEPJGVcnJywgsvvCAm6Ht7e/HVV1+JhWEtGQtlBRQXF6OhoQHAXybiPT09ZcciIkmCg4ORm5srjm/cuGEVOzyyUJ5SY2MjvvnmG/Hu45lnnkFsbKzsWEQkWVZWlpigHx0dxfHjx9Hf3y871qpioTwFvV6PM2fOoKurCwAn4onoL+6doG9sbLT4db5YKE/h+vXruH79ujjmRDwRGTKcoNfr9fj666/R0tIiO9aqYaE8oYmJCZw5c0bsJ82JeCK6l5OTk9Ed9FqtFsXFxbJjrRoWyhOqqKgQlwIqlUocPHiQE/FEdJ+QkBDs2LFDHF+6dAltbW2yY60KFsoTmJqaQkFBAaanpwEAycnJYjtQIqJ7ZWdni7MUnU5nsWcpLJQnUFFRgbq6OgCAg4MDcnNz4ejoKDsWEZkoPz8/ZGVlieOLFy/i7t27smOtOBbKY5qenkZBQYFYRXTjxo2Ij4+XHYuITNyOHTvERTu9vb24ePGi7EgrjoXymKqqqsRqwnZ2dsjNzYWzs7PsWERk4gICAsQVXwBw4cIFdHR0yI61olgoj2F2dtbo7CQxMREbNmyQHYuIzMSuXbsQEBAAAOjp6cHly5dlR1pRLJTHcOvWLWg0GnGcm5sLV1dX2bGIyEyoVCpkZmaK4/Pnz4sVyi0BC2WZ5ubmUFBQgPHxcQBAXFwckpOTZcciIjOTm5sLHx8fAEBXV5fRduHmjoWyTNXV1UZ7ROfm5sLd3V12LCIyM8HBwUhPTxfH586ds5hNuFgoyzA/P4+CggKMjY0BAKKjo5Gamio7FhGZIRsbG+Tm5oobobVaLa5cuSI71opgoSyDRqNBVVWVON61axfviieiJ6ZWq7FlyxZxXFhYiN7eXtmxnhoLZRkKCgrEml0RERFGp6tERI9r6ZaDpZWIOzs7jXZ8NVcslO/Q0tKCiooKcZyTkwNvb2/ZsYjIzEVGRmLz5s3i+Pz585iYmJAd66mwUL7DtWvXMDIyAgAIDAzE1q1bZUciIgugUCiQk5MDW9vFl+H29naz33uehfIIU1NTKCsrE8ebN2+Gn5+f7FhEZCFiY2MRGRkJYHG/FMPXG3PEQnmEhoYGtLe3A1i8MoNzJ0S0kpRKpdHryvXr1zEwMCA71hNjoTzCtWvXMDMzA2BxMj46Olp2JCKyMBkZGWLFDZ1Oh5qaGtmRnhgL5SGGhoaMTj/T09OhVCplxyIiCxMUFGS0n5I5D3uxUB5Co9Ggp6cHAODi4sLtfYloVdjZ2RkNe1VXV5vt+l4slIe4du2aeBwbG4vg4GDZkYjIQqWkpIgLfoaGhoxuVTAnLJQH6OnpQWVlpThOT0+Hvb297FhEZKF8fHyMFpstKyvDwsKC7FiPjYXyAJWVlRgcHAQA+Pr6ct0uIlp1aWlp4nFjYyNaW1tlR3psLJQHMJwU27hxI3x9fWVHIiILFx8fj9DQUADA+Pi4WU7Os1Du0dbWhrq6OnHMe0+IaC24ubkZnaVcu3YNU1NTsmM9FhbKPa5fvy6WqQ8JCUFCQoLsSERkJdLT0+Ho6Ahg8c1tQ0OD7EiPhYViYGZmxug0c8uWLdxEi4jWjFqtRlRUFABgdnbW7Ia9WCgGWlpaxESYg4MDh7uIaE05Ojoa3fN27do1MWJiDlgoBqqrqzE9PQ0ACA8PR0REhOxIRGRl0tPTxVIsPT09ZnW1FwvFgOFkfHx8vBjLJCJaKwEBAVCr1eK4trZWdqRlY6F8a3R01GgvgpiYGNmRiMhKGa7txUIxQ83NzRgeHgYAODs7IzY2VnYkIrJShoXS2NgotiA3dSyUb92+fVs8Dg4O5ja/RCRNVFQUPDw8AADDw8NoamqSHWlZWCjfMjyt5HAXEcnk4eEhdnIEjN/wmjIWChbnTwzfAXC4i4hkM8d5FBYKgKamJjFG6eDgwLvjiUi6DRs2iMfNzc1mMY/CQgGMttxUqVTw8fGRHYmIrFx4eLiYy713FMVUsVCwuDvjEg53EZEpcHZ2FsuwADCLveatvlBGR0eN7kSNj4+XHYmICMDi9hlLWChmoKmpCePj4wAAW1tbo3FLIiKZkpKSxOPW1laTn0ex+kIxbP3AwEDOnxCRyVCpVPD39wcATExMmPw8itUXSnV1tXjMq7uIyJTY29sbvS6Z+rCXVRfK9PS00fxJYmKi7EhEREaSk5PFY8MFbE2RVReKTqfD5OSkOOZy9URkagzvmG9vb5cd55GsulA6OzvFY4VCIcYqiYhMhb+/PxQKBQBgZGTEpDfcYqF8y8fHB05OTrIjEREZcXJyEhcLzc/Po6urS3akh7LqQtFqteJxUFCQ7DhERA9k+Ppk+EbY1Fh1oRj+YlQqlew4REQPZPj6xEIxUYa/GJ6hEJGpMnx9MhxZMTVWWyhjY2MYGRkRxywUIjJVHPIycV1dXZifnxfHHPIiIlNl+PrU3d1t9NplSqy2UAxbXqlUwsvLS3YkIqIH8vLyglKpBLC4BMvg4KDsSA/EQgEQEBAAe3t72ZGIiB7I3t4eAQEB4thUh72stlAMJ7Y43EVEps4crvSy2kLhFV5EZE7M4UovqyyU+fl5dHd3i2MWChGZOnO40ssqC2VwcBATExPimENeRGTqOORlonp7e42OeYZCRKbO8HWqv7/fJC8dtspCMVytU6FQwNXVVXYkIqJHcnV1hZ2dHQBgZmYG09PTsiPdxyoLxXAPFGdnZ9lxiIiWxcHBQTw2fB0zFSwUFgoRmQnDQpmampId5z5WWSiGvwgWChGZC56hmCCeoRCROeIZigky/EVwl0YiMhc8QzFBPEMhInPEQjFBY2NjmJqagl6vZ6HQihsfH0dTU5NJ/oMn82bqQ15WtcRuUVERblZU4dSpU2htbYWdnR3sFU4IDQ3F4cOHZccjM/fVV1/hZuUt9HR1oq+vD/7+/ggKVSN1UxJ27twpOx5ZAIVCIR6b4hsWqymU/+tf/ye+/roA9eN+GJoIgs26GCzop3GpYw7aX/8e5RWV+OF/+j5CQ0NlRyUz09XVhd//2x9QWFaL+j47TEzPw8bRAwu1Ong49yP+bBGul1fg737x32VHJTPHMxQT8Jvfvotf/T9/xEzILtiHpkLp5AkbByUW9DNYmBlDY1clat8/h7aWZvzud7/jnfO0bAMDA/j7v/97fHGlBbbhe2C3PgpKhRI2Di5YmBnD9OQQynsqUf3nQjg6OeFvfvpfZEcmM8Y5FMm+/vpr/Op//t+YCdsPx7jDsPMIgY2jG2BjBxuFM2xd/OC4PhcOG17DR/mlOHr0qOzIZEZ+//vf48+f5cM29mUoQrfC1sUPNg4uAAAbB1fYeQRDEf08ZsIP4Ne//f/w9ddfy45MZszUC8Xiz1D+129/iwH7ULiuz33k9ykCEuEUsx+//vWv8cILL8Df3192dDJxfX19ePfdd+EUdwCKgMRHfq8iIBGDjUH4zf/6Lfbu3Ss7OpkpDnlJND4+jpKSEihSfgbYKb7z+x3Vz6Cp9P/F7373O4SHh8uOTyaura0NnV3d8M5eXkHYBKahpOQ3GB8fh4uLi+z4ZIZ4hiJRS0sLRoaH4fMd7x6X2Lr4wt4tACdPnmSh0HdqbW2FvWsAbJW+y/p+RUAi+keG0dLSgsTE5f2dJDJk6mcoFj2HsrTU8wIWlv1nFhbmYWtr0f9baIXY2NhgYWFu2d+/sKAH8Je/l0SWxqLPUNRqNbx9fKHvvQ0714Dv/P65sR7MjemQl/dTqNVq2fHJxLW2tuIffvm/Y26sZ1l/v2Z7NPDw9EZYWJjs6GSmZmZmxGNTvCnbogvF2dkZ6enpOF/zDRxCMmCjePQvYKruNMJCg/G9730P3t7esuOTiRsYGMDvf/976OpOQ5n6/e/+A9oyZGc/A6VSKTs6mSnDQjHFdQgtulAA4Od/8zNce+MtTN7+AsqkNx76fTPackw15OPn/+c/IiDgu99tEgUEBODnP/85/tvf/w/Yq5LhoEp56PfOaMvhg178t5//UnZsMmOmfoZi8ZMFubm5+Jd//j/gP16JmepjmBtqw8LcX34pc2M9mG4uAuq/wE++/zreeust2ZHJjLz11lv4L99/Haj/AjPNRZgb6xFfW5ifg36wFbOaT+DUlo9//N/+O7Kzs2VHJjNm6oVi8WcoAPDjH/1nuHl44tSpM7jYcAIjs3ZQuPpjfmYCmOzDlihPvPDTV/F63qvw9PSUHdek6fV61NXVoaysDE1NTfD19UVKSgpSU1Ot8lJYT09P/MM//APCIz/GqaLruKmpxqyDB5zc/TE12AkX20mkBtvg+bdewffe5psVejoc8jIRf/V6HjbEx2LH1TJ8+MGf0dJRCXubOWzelIz/+tN3kJOTIzuiyZufn8fFixfxb//2b7CxsYGzszP6+/tx48YN1NXV4Y033rDKZWv8/f3xN//1p0jacB6VVbdQ31APrU4LdaIP4uLikbRxA7Zu3So7JlkAnqGYkOTkZCQnJ6NP14OzZ89CoVDgmaztLJNl6ujowG9+8xssLCzgxz/+MWJiYjA6Ooovv/wS7733HtRqNXbv3g0bGxvZUaXIyclBTk4O2tra0N7ejqioKKxbt052LLIgPEMxQf7+/mJoyxRvDjJVt2/fRktLC/75n/8Zu3fvFvfruLi44NSpUyguLsbOnTuNlti2RmFhYbw0mFbF7OyseGyKZygWPyn/IIbNzkJZvtDQUPzd3/0dtm3bZnTzp7OzM1xcXDA5OYmFheXfREpEj4dDXibI8BdhiuvhmKr4+HjEx8eL44WFBQwMDOD06dMYGhpCamqq1Z+dEK0mDnmZIMNfBAvlyXR3d+PDDz/EnTt3UF1djX379mHnzp1WO39CtBZM/QzFKoe8eIby9EZGRtDZ2YmhoSFMT09jcHAQOp2OQ15Eq8jUz1BYKCyUJxIQEICf/OQn+Md//Ef86Ec/wq1bt/Duu++it7dXdjQii2XqZygc8mKhPBEPDw94eHgAAMLDw9Hb24t//dd/xcsvv8yla4hWiakXilWeobi5uYnHer0eIyMjsiOZNScnJ6SkpKCvrw89PT1P/x8kovuMjIxgbm5xuwRHR0ejvVFMhVUWyr3voLVarexIJk+v1+PcuXM4evQoRkdH7/v60uXX1rj8CtFaMHyd8vX1Ncl9m0wv0Rrw8PAweuHr7OyUHcnk2djYoKGhAf/yL/+Cqqoqo8n3sbExXLp0CbGxsYiMjJQdlcgiGb5OBQUFyY7zQFY5h2Jra4vAwEDcuXMHAAtlOezs7LBt2zb88Y9/xG9/+1sMDQ0hLi4OIyMjKCoqwqVLl/DOO+8gIiJCdlQii2T4OqVSqWTHeSCrLBRgseGXCoVDXssTFxeHX/7yl/jwww9x9OhRODg4wM7ODhMTE3j++eeRl5fHIS+iVWL4OsUzFBNj2PA8Q1kehUKBffv2ITQ0FJWVlWhra4OnpydiY2ORlpbGpf+JVhGHvEyY4S+kt7cXs7OzXDZkGezt7ZGUlISkpCTZUYisxuzsrNE9XqZaKFY5KQ8Y/0ImJycxMDAgOxIR0QMNDAyIe+ZcXFzEPWCmxmoLZd26dUaX3XEehYhMleHrU2BgoEleMgxYcaG4uLgYjflzHoWITJU5zJ8AVlwogPEvhoVCRKbKHC4ZBlgo4jGHvIjIVJnDJcOAlRcKLx0mInPAMxQzYPiLMbyKgojIVBhehbq0yoepsupCMTx11Ov1XCmXiExOT08P9Ho9gPvXITQ1Vl0ovr6+Rr+c5uZm2ZGIiIwsLREFAGq1WnacR7LqQnF0dDRaHff27duyIxERGbl165Z4HB8fLzvOI1l1oQDAxo0bxWONRiM7DhGRoNfrjV6XNmzYIDvSI1l9oSQmJorH3d3d6Ovrkx2JiAgA0NXVBZ1OBwBwd3fnkJepU6vVcHd3BwDMzc2hrq5OdiQiIgBAdXW1eBwVFQWlUik70iNZfaEolUpER0eLY86jEJGpMJw/MfXhLoCFAsD4F8V5FCIyBRMTE0YjJqY+IQ+wUAAs7kS4pLOzk/MoRCRdW1ubuKHRy8sLoaGhsiN9JxYKgNDQUHh5eQEAZmZmUF9fLzsSEVk5w+H3mJgYk58/AVgoABbnUWJiYsQxJ+aJSDbD4feEhATZcZaFhfItw/FJFgoRyTQ8PIzGxkZxbPiG15SxUL4VGxsrHre3t6O/v192JCKyUnfu3MHw8DAAwMfHxyzmTwAWihAaGgofHx8Ai6t78iyFiGQxnD+JjY01i/kTgIUiKJVKo7MUTswTkSz3TsibCxaKAcNfXHV1NfdHIaI1p9Vq0draKo4N3+iaOhaKgQ0bNsDJyQnA4jxKU1OT7EhEZGVKS0sxPj4OYHETQHOZPwFYKEZCQ0PFcvazs7MoLS2VHYmIrMjU1BTKysrEcXp6utnMnwAsFCMKhQJpaWni+MaNGxgaGpIdi4isRHNzsxgZcXBwMHo9MgcslHukpaWJ1Ye1Wi1qampkRyIiK1FaWoqZmRkAQHh4ONavXy870mNhodwjKCjI6CZHw9NPIqLVMjw8jOvXr4vj9PR0ODo6yo71WFgoD2B4mlldXY2enh7ZkYjIwmk0GnR2dgIAXF1dzW64C2ChPFBSUhJ8fX0BAAMDA7hx44bsSERk4QxHQ2JjYxESEiI70mNjoTyAn58fNm3aJI5LS0sxOzsrOxYRWaje3l6jzbTS09NhY2MjO9ZjY6E8hOHpZkNDA9ra2mRHIiILVV5eLtYP9Pb2RnJysuxIT4SF8hBxcXEICgoCsLi2FyfniWg16PV6o3vekpKSEBAQIDvWE2GhPIS7u7vRWUppaSnGxsZkxyIiC9Pe3o6GhgZxbI6T8UtYKI9geNlee3s7VyAmohVXVlYmllpZt26d2Wym9SAslEeIjIxEeHg4AGBhYYHDXkS0osbHx42Gu9LS0uDp6Sk71hNjoTyCo6Oj0elnRUUFuru7ZcciIguh0WjEBT/3Lv1kjlgo3yE9PV28Y+jt7cXly5dlRyIiCzAzM4OioiLMz88DWFxqJSoqSnasp8JC+Q4hISFITU0Vx8XFxdDpdLJjEZGZq6+vR1VVlTjeuXMnnJ2dZcd6KiyUZcjNzYWHhwcAoK2tDVevXpUdiYjMmF6vR2FhoZiMDwsLM/vhLoCFsiwxMTFGd84XFRWJm5CIiB7XnTt3UFFRIY5zc3PFck/mjIWyDLa2ttizZ49Y1r65uRnXrl2THYuIzNDCwgIKCwsxPDwMYHFjv4yMDNmxVgQLZZliY2ONlkM4e/YsN98iosfW0tJitODsrl274O/vLzvWimChLJOdnR12794NV1dXAEBjYyPKy8tlxyIiM1NYWIjBwUEAixf9bN26VXakFcNCeQzx8fFISkoSx4WFhRgZGZEdi4jMRHt7u9Fw+c6dO8123a4HYaE8Bnt7e+zevRsuLi4A7r/sj4joUc6dOyduOwgKCrKosxOAhfLYEhISsGHDBgDA3Nyc0aV/REQP09nZaXTLQU5ODgIDA2XHWlEslMfk4OCA3bt3Q6lUAlhcOqGmpkZ2LCIycRcuXBBLN6lUKmzfvl12pBXHQnkCGzZsQGJiIgBgdnYWhYWFmJyclB2LiExUV1eX0bJN2dnZUKlUsmOtOBbKE3B0dERubq5YJqG6uhrV1dWyYxGRibpw4QI6OzsBAIGBgcjKypIdaVWwUJ7Qxo0bERcXB2BxR8cTJ05gYGBAdiwiMjHNzc0oLi4Wx1lZWQgODpYda1WwUJ6Qs7Mznn/+ebEScXV1NVciJiIjk5OTOHnyJLRaLYDFu+Kzs7Nlx1o1LJSnsGnTJqMlEwoLC9He3i47FhGZiIqKCnHfib29Pfbt24eQkBDZsVYNC+Up2NnZGf0FaWtrw5kzZzAzMyM7GhFJptPpcPLkSYyNjQFYvDHa0u47uRcL5SmFh4dj3759UCgUAIArV65wgp6IcOHCBdy+fRsA4OHhgcOHD8PLy0t2rFXFQlkB27ZtQ0JCAgBgeHgYx48f5wQ9kRVraWlBUVGROE5PTzdaXNZSsVBWgJeXF1566SV4e3sDAG7duoWSkhLZsYhIgqWJ+KXLhFUqFfbt2wc7OzvZ0VYdC2WFbNy40ejO14KCAk7QE1mhyspKlJWVAQBsbGyQm5uLyMhI2bHWBAtlhdjY2GD37t0ICwsDwAl6Imuk0+lw4sQJMREfFRWFZ555RnasNcNCWUGhoaF47rnn4OjoCGBxgp7rfBFZj+LiYjER7+LigkOHDsHPz092rDXDQllhW7duxcaNGwEsTtB/8cUXnKAnsgItLS04d+6cON68eTNSU1Nlx1pTLJQV5u7ujsOHD8PX1xcAJ+iJrMH4+LjRRLy/vz8OHDgAJycn2dHWFAtlFSQmJhqNmxYUFKC+vl52LCJaJWVlZWIiHgB27NiB2NhY2bHWHAtllTz77LPiyo62tjYcO3ZMrOdDRJajsbHRaCI+MjISOTk5smNJwUJZJcHBwcjLyxMTcjdv3sTp06cxOjoqOxoRrZCenh4cO3YMLS0tABaHuvLy8hAUFCQ7mhQslFWUlpaG3NxcODg4AADOnz+PK1euyI5FRCtgamoK33zzDW7cuAFgcQXyvXv3Ij09XXY0aVgoq2jppqbNmzcD+MvEXW1trexoRPSUysvLja7qSk9Px7PPPis7llQslFXm4+ODI0eOICIiAgBw9+5dfPjhh+jo6JAdjYieUFNTEz7//HMMDg4CAGJiYnD48GGxP5K1YqGsgejoaLzyyivw8fEBAFRVVeHEiRMYHh6WHY2IHlNfXx8+/vhj3LlzB8DiWl2vvfYawsPDZUeTjoWyRjIyMrBr1y6xzP3Fixdx6dIlzM/Py45GRMs0MzODs2fPikuEXV1d8fzzz4thbWvHQlkjtra22LNnj1jCenJyEqdPn+bSLERmpLKyEgUFBVhYWACwuHWFtV4i/CAslDXk5+eHl19+GWq1GgCg1Wrx0UcfcVViIjPQ2tqKzz77DH19fQAWd2B84YUX4OLiIjuayWChrLHY2FgcOXJE7J1SU1ODL774QkzuEZHpGRwcxGeffYa6ujoAQEhICF5//XWL3h/+SbBQJFg6Tba3twcAXLp0CWfPnsXExITsaER0j4mJCZw9e1bcQ+bp6YlDhw6JRWDpL1goEtjZ2WHv3r3iL+Ts7CzOnDmDixcvQq/Xy45HRN/S6/W4ePEizpw5A71eDzs7O2RnZ1vVHiePg4UiSUBAAF555RWx3tfAwAC++OILlJaWyo5GRN8qLS012oJi06ZNRnsekTEWikTx8fF49dVXERwcDADo7u7GsWPHcPPmTdnRiKzezZs3cezYMXR3dwMA4uLikJeXh3Xr1smOZrJYKJJlZGTglVdeQUBAAIDFO+mPHj2Kqqoq2dGIrFZVVRWOHj2Ku3fvAgDWr1+PN954A9HR0bKjmTQWignYsWMHXnrpJXh5eQEAmpub8ec//xkajUZ2NCKro9Fo8Oc//xnNzc0AFrf2zsvL4yT8MrBQTMTevXtx4MABcU17Q0MDPvjgA7G8AxGtvjt37uCDDz5AQ0MDAGDdunV4+eWXkZaWJjuaWWChmJBDhw5h9+7dYnmWmpoaHDt2TGwrSkSrp7OzE8eOHROrV3h7e+Oll15Cdna27Ghmg4ViQuzt7fHyyy8bXZJ4/fp1fPrpp+IqEyJaeQMDA/j0009x/fp1AItrdB0+fBh79uyRHc2ssFBMjKurK958802jTXqKiopw/PhxTE5Oyo5HZHEmJydx/PhxFBUVAQAcHBzwwgsv4ODBg7KjmR0Wigny8fHB22+/jU2bNonnTpw4gVOnTsmORmRxTp06hRMnTojjPXv2IC8vT3Yss8RCMVFBQUH467/+ayQmJorn3n//feTn52NmZkZ2PCKzNz09jfz8fLz//vviuR07duCtt96SHc1s2SwsrcNMJqm2thbvvfce6uvrxXPvvPMOcnNz4erqKjsekVkaGRlBYWEh/vSnP4nntm7dih//+Mdwd3eXHc9s2f3TP/3TP8kOQQ/n5+cHPz8/9PT0iGWzKysroVAoEBwcDGdnZ9kRicyKTqfDmTNn8OGHH4rntm7diu9973tiFXB6MiwUMxAYGIiAgAAMDg6KZSCWLm1UqVQ8UyFapo6ODpw8eRJffvmleC4nJwdvv/02/P39Zccze/ayA9DybNy4Ea6urnBycsLVq1cBAF9++SWmpqZw4MAB7stA9B2amppw8uRJnD9/HgDg6OiIrKwsfP/73+cmWSuEcyhmpqenB3/6059w+fJl8Vx2djYOHTokVi4mImO1tbU4fvy4WM3b09MTOTk5eOONN+Dg4CA7nsVgoZihgYEB/Md//AdKS0sxPT0NAEhPT8dLL72E2NhY2fGITIZer0dNTQ0+/fRTVFdXA1hcTmXPnj148cUXYWNjIzuiRWGhmKnR0VF89NFHuHTpEoaGhgAASUlJePnll5GYmAhbW14RTtZtfHwcN2/exBdffIGmpiYAgFqtxnPPPcc74FcJC8WMTU1N4fTp0ygoKBCT9dHR0Xj55ZeRlJQEJycn2RGJpBgYGMDly5dx5swZdHV1AQAiIyNx5MgRbNu2TXY8i8VCMXNzc3M4e/YsvvzyS7GIZEhICA4dOoQtW7bA09NTdkSiNaXValFYWIizZ89ieHgYABATE8NVg9cAC8VCLK331dbWBgDw9fXFrl27kJ2dLXaEJLJ0DQ0N+Oabb3DhwgXMzs4C+MvOqIZLGdHqYKFYkEuXLuHzzz8XGwMpFAps27YN+/btQ0xMDOdVyGKNj4+jvr4eJ0+eNNpCe8OGDXjttdeMljCi1cNCsTClpaX48ssv0dDQAL1eD2DxHpYDBw4gPj4ebm5usiMSraienh6Ulpbi7Nmz4gzdzc0N0dHRyMvLQ0xMjOyIVoOFYoFqamrw1VdfQaPRYHBwEAAQHByMnJwcbNu2DSqVSnZEohVx584dFBQUoKSkBKOjowAWV4/YunUrcnJyeMPvGmOhWKju7m5cunQJxcXFaG9vBwA4Oztj27Zt2Lt3L6Kjo2VHJHpik5OTqK+vx6lTp8SmWDY2NoiOjsaePXuwbds2rnMnAQvFgun1epSUlCA/Px+NjY1iknLz5s144YUXEBMTwyUnyOzodDqUl5fjm2++EfeXuLu7IyYmBgcOHEBycrLsiFaLhWIFNBoN8vPzUVNTI7YSDgsLw7PPPouMjAwEBATIjki0LC0tLSgsLMTly5fFDb1BQUHYvn07r2g0ASwUK9HT04OSkhIUFRWJITBXV1ds374de/bs4TpgZNKmp6fR0NCA06dPi8VRbW1tER0djb1792Lbtm1wdHSUHdPqsVCsyPz8PEpKSvDVV1+hoaFBDIGlpaXh+eefh1qt5o2QZHJ6enpQU1OD/Px8NDQ0AAA8PDwQFxeH559/Hhs3bpQdkb7FQrFCtbW1yM/PR3V1Nfr7+wEAERERSElJQWZmJsLDw2FnZyc7Jlm5sbExtLa24uLFi7hx44bYYC44OBhZWVnIzs7mFYsmhoVipXQ6HUpKSnDu3Dlx7b6NjQ1SU1ORnZ2N6OhorFu3TnZMslKtra0oLy9HWVkZ6urqACzeqLt+/XoxxMVl500PC8WKLSws4MqVKygsLERbW5s4W/H19UVKSgqys7OhVqu5IyStmb6+PrS0tODcuXMoLy8X2zOoVCrExcVh586d2LBhg+yY9BAsFEJ7eztu3ryJkpIStLW1YWpqCsDignoZGRlISUmBWq2WHZMs2NTUFFpbW3H58mXcuHEDWq0WwOJGWGFhYcjOzkZKSgq8vLxkR6VHYKGQcOvWLZSUlKCmpgZ3794FADg4OCA1NRW7du2CWq2Gn5+f7JhkYTo6OsTfvaVNsBQKBdRqtXhDExERITsmLQMLhYyMjo6ivLwcFy5cQGtrq7hvJTAwEKmpqdi+fTvUajXvQqanNjg4iNbWVpw/fx43btzA2NgYgMXhrdjYWGRlZSElJUV2THoMLBR6oPb2dpSXl+PKlStGw2AbNmzA1q1bsXHjRgQHB3MLVXps09PTaG9vx5UrV1BeXo7W1lYAHN6yBCwUeqSqqipcuXIF1dXV6OjoALB4Q2RKSgq2bt2KoKAgqFQq2Nvby45KJm5ychJarRYNDQ0oKysTy8wrFAqEhYUhMzOTw1tmjoVC32lpGOz8+fNoa2sTw2C+vr6Ij48Xk/YqlYp3K9N9xsfH0dnZidraWty6dQsajQYTExMAOLxlaVgotGxLw2ClpaXQarVie1UPDw/Ex8cjOTkZUVFRUKlUUCqVsuOSZKOjo9BqtaiurkZ1dTU0Gg1mZmYAAH5+flCpVBzesjAsFHpsNTU10Gg0qKiogFarFYv0KZVKxMfHY+PGjYiLi4NKpeKGXlZoeHgYWq0WlZWV0Gg00Gg0mJubAwAEBARApVJhy5YtSEhIQHh4uOy4tIJYKPTEamtrodFocPPmTWi1WjEUZm9vj4SEBMTHxyMpKQkqlYprhFmBwcFBaLVaVFRUoKamBrdv3xZfCwwMhEqlQlpaGhISEhAaGio7Lq0CFgo9tYaGBmg0GpSXl0Or1Yo1lwAgPj4e8fHx2LRpE1QqFXx8fGTHpRXW19eHrq4ulJeXQ6PRoL6+HsDiUj4qlQoqlQrp6elISEhAUFCQ7Li0ilgotGKam5tRU1Mj7nTu7e0VX4uKikJCQgKSkpLg6+sLX19fbu5lxsbGxtDX14f+/n4xtHXnzh0AgJ2dHVQqFYKCgpCeno7ExETuuWMlWCi04tra2qDRaHDt2jVotVp0d3eLrwUGBiIiIgIRERGIjo4W5cKrw0zf5OSkKJGGhgY0NzejpaUFXV1dABYv/w0MDERYWBi2bNmCxMRE+Pr6yo5Na4iFQqumo6MDGo0GZWVl4oxFr9eLr6vVakRERCAqKgpqtVqUC5fONx0zMzOiRJqamtDc3Izm5maxSRsAODs7Y926dQgPD0dqaioSEhJ41ZaVYqHQquvq6oJGo0FNTQ20Wi10Op1Y2RhYfGe7dNYSFxeHwMBA+Pr6cr5Fkrm5OVEi7e3taGxsFGcj8/PzABaHtXx9feHn54f169cjLi4OiYmJvKrPyrFQaM2Mj4+jubkZTU1NqKmpQX9/P3Q6HUZGRsT3uLq6inJJTEyEj48PfH194eHhITu+xevv70dfXx+6u7tRW1srSmRpCXkA8PLygp+fHwIDAxEfH4/169cjIiKCZ5UEgIVCkvT394tyqaurQ19fH/r6+sQd1ADg4+MjyiUqKgru7u7w8PCAh4cHb5xcASMjIxgeHhafa2tr0dLSgubmZrFQI7BY8kvDkQkJCaJEeDZC92KhkHSdnZ1obm7GnTt3cOfOHVEuS3veA4vlsnQvg0qlQkhICNzd3eHp6QkvLy/u3rcMExMTGBgYEAXS2toKrVaLrq4udHV1YXR0VHyvg4ODGNKKiYlBREQEIiMjebUWPRILhUzGwsKCmPitq6tDR0eHKJd7LQ27BAUFITQ0FAEBAfDw8ICXlxe8vLw4BIPFVX0HBwcxODgo7l5vb28XJbK0dI6hpTOR0NBQxMbGYv369dxcjZaNhUImaXJyUpSLRqMR76qHh4eN3kkv8ff3F+USGhoKHx8fUS5KpdIqzmAmJycxPj4uSqSnpwft7e24e/eu0RI5htzc3MQworu7OxISEhAZGYnIyEg4OTnJ/pHIzLBQyOQtLTK49NHe3o7BwUFRMuPj4/f9mcDAQFEu3t7ecHd3h1KphFKphLOzs3isVCpha2sr+0dcNr1ej4mJiQd+DA0Noa+vD+3t7WhvbxdL4RhycXER5eHl5YXQ0FAxjMi11+hpsVDI7IyMjIh33VqtFp2dnRgaGsLQ0BCGh4cxOTl5359xcHCAt7e3OGvx9vYWxy4uLg8sGpk3W05MTGBycvK+0hgdHRVnIAMDA0afly7pNeTs7AwPDw94enrC09NT7F9jOA9FtFJYKGT2lgqmo6MDHR0d6OnpEQUzOjqKiYkJPOqv+dK79XsLx93dHXZ2dkYf9vb29z33sK/Pzc1hbm4Oer1ePF7ucw8qjMHBQaOr4O5la2sLZ2dnuLm5iQIJCAhAcHAwgoODWSC06lgoZHEMC6anpweDg4MYHx83ete/9Hlpa+MHsbGxgYODAxwcHKBQKB74+VFfn52dxczMjPhs+PGgrxk+fpSlMylnZ2ejxy4uLvDy8hIlwgKhtcZCIaswMjIi3u0PDQ2Jd/3Dw8NGQ0qGhWN42fJac3R0fGBpKJVKeHl5iculDT84/0GysVDIqi0NL907tLQ0vLQ0FDU/P2/0+d7hqgd9LGdY7GFfd3NzE0Xh6ekphuM8PT1hY2Mj+38b0QOxUIgeYm5u7r6hqQcNUT3suYcNiz1s6MzwMUuDzBELhYiIVoT5XIBPREQmjYVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQrgoVCREQr4v8HGUAeK5tqC9oAAAAldEVYdGRhdGU6Y3JlYXRlADIwMTktMDEtMThUMDU6MzE6NTgrMDA6MDDnRTd0AAAAJXRFWHRkYXRlOm1vZGlmeQAyMDE5LTAxLTE4VDA1OjMxOjU4KzAwOjAwlhiPyAAAAABJRU5ErkJggg==)
ii. Now, extend the diameter to A and B on both the sides.
![](data:image/png;base64,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)
iii. Then, draw the perpendicular bisectors of OA and OB.
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Such that:
Perpendicular bisector of OA intersects it at point O’.
And,
Perpendicular bisector of OB intersects it at point O”.
![](data:image/png;base64,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)
iv. Considering O’A as radius, construct another circle.
v. considering O”B as radius, construct the third circle.
vi. From point A, draw tangents AP and AQ.
vii. From point B, draw tangents BR and BS.
Question 4.Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Answer: Steps of construction:
1) Draw a circle of radius 5 cm, and draw a radius OA anywhere in the circle.
![](data:image/png;base64,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)
2) Taking OA as base, draw an angle AOB such that ∠AOB = 120°.
![](data:image/png;base64,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)
3) At A, Draw a line AX such that AX ⊥ OA.
![](data:image/png;base64,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)
4) At B, Draw a line BY such that BY ⊥ OB.
![](data:image/png;base64,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)
5) AX and BY intersect at P; AP and BP are required tangents.
Justification:
1) Clearly, AP and BP are tangents since tangent at a point on the circle is perpendicular to the radius through point of contact.
2) In Quadrilateral OAPB, we have
∠OAP + ∠APB + ∠OBP + ∠AOB = 360° [By Angle Sum Property]
⇒ ∠OAP + 90° + 90° + 120° = 360°
⇒ ∠OAP = 60°
Question 5.Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Answer:Step1: Draw a line PQ=8cm. taking P and Q as a center draw circle of 3cm and 4cm.
Step2: Now bisect PQ. We get midpoint of PQ be T.
Now take T as a center , draw a circle of PT radius , this will intersect the circle at point A,B,C,D. Join PB,PD,AQ,QC.
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Justification:
It can be justified by prove that PB,PD are tangents of circle (whose center is P and radius is 3cm) and AQ,QC are tangents of circle (whose center is Q and radius is 4cm)
Join PA, PC, QB, QD
∠PBQ=90° (Angle is on semicircle)
BQ⊥PB
Since, BQ is radius of circle, PB has to be a tangent. Similarly PD, QA ,QC are tangents.
Question 6.Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
Answer:Step1: Draw a circle from a bangle.
Step2: Take a point A outside the circle and two chords BC and DE.
Step3: Bisect chords. They intersect at point O.
Step4: join OA and bisect it. We get midpoint of OA is P. Taking P as a center draw a circle of OP radius which intersect circle at W and X.
Join AW and AX. These are tangent.
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Justification:
We have to be proved that O is center of circle.
Join OW and OX.
∠AWO=90° (angle is on semicircle)
OW is perpendicular to AW.
Since, OW is radius of circle, AW has to be tangent. Similarly AX is tangent.
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer:
Step1: Draw circle of radius 6cm with center A, mark point C at 10 cm from center
Step 2: find perpendicular bisector of AC
Step3: Take this point as center and draw a circle through A and C
Step4:Mark the point where this circle intersects our circle and draw tangents through C
Length of tangents = 8cm
AE is perpendicular to CE (tangent and radius relation)
In ΔACE
AC becomes hypotenuse
AC2 = CE2 + AE2
102 = CE2 + 62
CE2 = 100-36
CE2 = 64
CE = 8cm
Question 2.
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Answer:
Steps of construction:
i. Draw two concentric circles with radii 4 cm and 6 cm respectively.
ii. Now, draw the radius OP of the larger circle.
iii. Construct a perpendicular bisector of OP intersecting OP at point O’.
iv. Considering O’P as radius, draw another circle.
v. From point P, draw tangents PQ and PR(can see in the figure)
Justification: By applying Pythagoras theorem, we have;
PQ2 = OP2 – OQ2
= 62 – 42
= 36 – 16 = 20
Or, PQ = 2√5 cm
Question 3.
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Answer:
Steps of construction:
i. At first draw a circle with radius 3 cm.
ii. Now, extend the diameter to A and B on both the sides.
iii. Then, draw the perpendicular bisectors of OA and OB.
Such that:
Perpendicular bisector of OA intersects it at point O’.
And,
Perpendicular bisector of OB intersects it at point O”.
iv. Considering O’A as radius, construct another circle.
v. considering O”B as radius, construct the third circle.
vi. From point A, draw tangents AP and AQ.
vii. From point B, draw tangents BR and BS.
Question 4.
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
Answer: Steps of construction:
1) Draw a circle of radius 5 cm, and draw a radius OA anywhere in the circle.
2) Taking OA as base, draw an angle AOB such that ∠AOB = 120°.
3) At A, Draw a line AX such that AX ⊥ OA.
4) At B, Draw a line BY such that BY ⊥ OB.
5) AX and BY intersect at P; AP and BP are required tangents.
Justification:
1) Clearly, AP and BP are tangents since tangent at a point on the circle is perpendicular to the radius through point of contact.
2) In Quadrilateral OAPB, we have
∠OAP + ∠APB + ∠OBP + ∠AOB = 360° [By Angle Sum Property]
⇒ ∠OAP + 90° + 90° + 120° = 360°
⇒ ∠OAP = 60°
Question 5.
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Answer:
Step1: Draw a line PQ=8cm. taking P and Q as a center draw circle of 3cm and 4cm.
Step2: Now bisect PQ. We get midpoint of PQ be T.
Now take T as a center , draw a circle of PT radius , this will intersect the circle at point A,B,C,D. Join PB,PD,AQ,QC.
Justification:
It can be justified by prove that PB,PD are tangents of circle (whose center is P and radius is 3cm) and AQ,QC are tangents of circle (whose center is Q and radius is 4cm)
Join PA, PC, QB, QD
∠PBQ=90° (Angle is on semicircle)
BQ⊥PB
Since, BQ is radius of circle, PB has to be a tangent. Similarly PD, QA ,QC are tangents.
Question 6.
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
Answer:
Step1: Draw a circle from a bangle.
Step2: Take a point A outside the circle and two chords BC and DE.
Step3: Bisect chords. They intersect at point O.
Step4: join OA and bisect it. We get midpoint of OA is P. Taking P as a center draw a circle of OP radius which intersect circle at W and X.
Join AW and AX. These are tangent.
Justification:
We have to be proved that O is center of circle.
Join OW and OX.
∠AWO=90° (angle is on semicircle)
OW is perpendicular to AW.
Since, OW is radius of circle, AW has to be tangent. Similarly AX is tangent.