Class 10th Mathematics Gujarat Board Solution
Exercise 12.1- Draw bar ab of length 7.4 cm and divide it in the ratio 5 : 7. Construct the…
- Divide a line-segment into three parts in the ratio 2 : 3 : 4 in the same…
- Construct a triangle with sides 4 cm, 5 cm, 7 cm and then construct a triangle…
- Draw ΔPQR with m∠P = 60, m∠Q = 45 and PQ = 6 cm. Then construct ΔPBC whose…
- Draw ΔABC having m angle ABC = 90, BC = 4 cm and AC = 5 cm. Then construct…
- Draw bar pq of length 6.5 cm and divide it in the ratio 4 : 7. Measure the two…
Exercise 12- Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct…
- Draw ⨀ (O, 4). Construct a pair of tangents from A where OA = 10 units.…
- Draw a circle with the help of a circular bangle. Construct two tangents to…
- Draw ⨀(O, r). bar pq is a diameter of 0(0, r) . Points A and B are on the bar…
- Draw AB such that AB = 10 cm. Draw ⨀(A, 3) and ⨀(B, 4). Construct tangents to…
- ⨀ (P, 4) is given. Draw a pair of tangents through A which is in the exterior…
- Draw bar ab of length 7.4 cm and divide it in the ratio 5 : 7. Construct the…
- Divide a line-segment into three parts in the ratio 2 : 3 : 4 in the same…
- Construct a triangle with sides 4 cm, 5 cm, 7 cm and then construct a triangle…
- Draw ΔPQR with m∠P = 60, m∠Q = 45 and PQ = 6 cm. Then construct ΔPBC whose…
- Draw ΔABC having m angle ABC = 90, BC = 4 cm and AC = 5 cm. Then construct…
- Draw bar pq of length 6.5 cm and divide it in the ratio 4 : 7. Measure the two…
- Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct…
- Draw ⨀ (O, 4). Construct a pair of tangents from A where OA = 10 units.…
- Draw a circle with the help of a circular bangle. Construct two tangents to…
- Draw ⨀(O, r). bar pq is a diameter of 0(0, r) . Points A and B are on the bar…
- Draw AB such that AB = 10 cm. Draw ⨀(A, 3) and ⨀(B, 4). Construct tangents to…
- ⨀ (P, 4) is given. Draw a pair of tangents through A which is in the exterior…
Exercise 12.1
Question 1.Construct the following with the help of straight-edge and compass only:
Draw
of length 7.4 cm and divide it in the ratio 5 : 7.
Answer:Steps of Construction:
1. Draw a line AB of length 7.4cm
![](data:image/png;base64,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)
2.Draw a ray AX making an acute angle with AB.
![](data:image/jpeg;base64,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)
3. We have to divide line in ratio of 5:7. So we make 5+7 =12 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A12.
![](data:image/jpeg;base64,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7. Join A12 with B.
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8. As we have to divide in 5:7, we draw a line from A5 parallel to A11B.
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9. The point where it cuts AB is P.
Question 2.Construct the following with the help of straight-edge and compass only:
Divide a line-segment into three parts in the ratio 2 : 3 : 4 in the same order.
Answer:Steps of Construction:
1. Draw a line AB of any length.
![](data:image/png;base64,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)
2.Draw a ray AX making an acute angle with AB.
![](data:image/jpeg;base64,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)
3. We have to divide line in ratio of 2:3:4. So we make 2+3+4 =9 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A9.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCAD7AVwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKrS30EN7DaSMVknBMeRw2Ooz698VZrB8RqdQEWkWvF3KRKsoz/owU/wCs479h65rSnFSlZ7CZrWt7DeNMIGLiFzGzY4LDqAe+KsVleHp0Oniz8kW89mfKmhHZvUeoPXPvWrSnHlk0MKKKKgAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAopkkiRRtJI6oijLMxwAPUmsn7deawdumZtrQ9b2ReX/65qev+8ePQGgA8RarNaWU1tpn77VZI8wQou5h/tEdAB6niq3g2TXJtMkbXUcS+biIyoFkZMfxAe+cVr2Gm22nRstuh3Od0kjnc8h9WY8k1bq1O0HG3z6i6iYAOcc0tFFQMKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKrX119jtHm2b2GAiZxuYnAH500m3ZAWaKr2V0t5aRzqNu4cr/dI4I/A1zuueOINE8QQ6XLaM6Ns82YuF27jgYHf35FXGnOcnGK1Fc6qikFI7rGjPIwVFGSzHAArMY6qN/qsNk6wKr3F3IP3dtEMu3uf7o9zxVQ395q5KaT+5tv4r6Rfvf9c1P3v948fWr1hpttpyMIVJkkOZJZDueQ+rN3oApx6VPfyLcayyyBTujs0P7qM+/98+549BWt0paKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAopiyxuzKjqzIcMAclT70kk8MO3zZUj3ttXcwG4+g96AJKzNRtri9vLaJGeGGImVpVAPzDhRz9Sa0qWqjJxd0BhxG60iaa3Cm4W4lUwu5Cje2dwOOnTPTvVqOGz1Ys95Y28k9uzRNvQPt9cEjoQal1SIS2TZaFVQh2M33MDrk9vr2rndPutQ1KF4NACQW0khaXU3jPl+mIUPL9PvH5frWkpKUbvcQtv4ht9E1WXREWe8iU7bXYuSj/APPEk9cdieg4J4rWTS7jUXWfWmVkByllGcxJ6bj/ABn68e3eqLeBtNWJ2SW6e6ILpPNOWIl6iQ/7Wfw9q1tF1JdU02OclBMPknjDA7JBwwPpyDWcuXTlGXwMDA4ApaKKkAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKiup0tbaS4kOFjUsfwqWo54IrmIxTIHQ4yp6HFNWvqBz2lyS2l/A81vPEb0FZnkUAGQksuOfTI/Kqvivwwniy7ga21SKKS1DI6Eb9uT94AHg11NxBHPHtkjEgUhlU+o5FYGlOkV1bO0ysscMnmKV2/Zh1O49/Tn611RqNv2kdGv6/4BNuhf0rUJVl/svUFEd7EmVYH5bhBxvU/wAx1H607VtftNKZLcrJc3sw/c2cA3Sye+Ow/wBo4Arm9bnvPFskB0K1kns7Vmb7WZPKWR+g8s9WA5yRx9a2PCFhaW+lC4WNjfSkrezSsXlaVThgzHng9B0xXM4pRTuMbHoV5rUi3PiR0aMHdFpkTZhT08w/8tG+vyj0710KqFUKoAAGAB2paKkY113oy5IyMZHUVy/hPwa/hq+url74TiZdiqqbcjOdzc8t/wDXrqqKuNSUYuK2e4rBRRRUDCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAKepXclrbZgVXnkcRxK3QsfX26mn2F0LyzjnxtZh8y/3WHBH51XvLCS91CFpGZLeFCV2OVYueO3oP51BHaXGmC78q4SO13ecHlBkI4+YHkdxnNbKMHC19RGR4j8Xaho3iS006GxR7eYoC753SFmxhT0GPfNdfWYq/a9EdtXjjeN0ZpE2YATryPXFczpHiTVNSI0XTlRJNpeK9u3DFYOACUH3nGQPTuT2okrx92O27A6fVtcs9JEaS75rmbiC1hXdLKfZfT1JwB3NZyaJe65Itx4jKrbg7o9LibMY9DK3/LQ+33R6HrWhpOhWulGSZWkuLyYDz7uc7pZfqew9FGAPStOsRjVVUQKoCqBgADAAriYtdvrL4h3OlxWB+y3cq7xtOR8nMoPTBwM/T1ruKTFXCUY3ur/1uIWiiioGFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFVTqFv8A2h9h3Hz9m/GOMfX1qw7BFLMcADJNc0Uv2tjqwjiI877SBlvM2Djbjp92tacFK9/6YmdBdXtrYw+dd3EVvHkDfK4UZ9MmpVZXUMjBlYZBByCK5fxNptt4pjt4FkuIRDN8twsYdAzDkEZB6Hr2NXdCf+xootBvHVZLeL/R5ScC4jHUj0Ydx+I4olCKgnfXsBuVkeItSsbOzEF1K5luGAit4U3yzYOdqr3+vQd6qya9d6zI1r4aRHjB2yanKMwR+oQf8tG+nyjue1XtJ0C10t3uC0l1fTD99eXB3Sv7Z/hX/ZGBWadncZnjSNR8QESa+fs1l1TS4XyGH/TZx97/AHR8vrmnapo9jpGntqOm2kNtNZP9oyg27lA+Zc+hUnj6V0VUdZ0uPWtJuNOlkaNZ1xvXqDnIP5iiO9nsBPZ3ltf2yXNpMk0LjKujZBqesbwz4eTw5prWi3DXDSSGR3K7QSQBwO3QVs05qKk1F3QBRRRUgFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUlYsOpTNq+5pVNnLI1uiccMB978TkVcYOV7AbdFZ+ty38GjXUumRiW8WMmJCM5P07nHasjwbrGpXtvLa62HjvkbdGssXlu8Zx82MDPORkUKDcHO/wDmK501GKKwJ9eudTmez8ORpOUJWW/lBNvCe4GP9Y3sOB3IqBlTU5odEuQ0yMZ57rzIGibdLKDyUVByT29Ockis7UfCms+JJ5b++W0tPOUBLV8ytEo6KT0ye4HAz3rqNK0G20yR7p5JLu/mGJryc5kb2HZV/wBkYFada+1le6FYpaNdRXelQSxQrAAuxoVGBEy8FcexBFXq4vQpPEUXjW/t57R49NllkkYmPCDsrK3cnAyPc9K7SpnBwaTYJhRRRUDCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKiubiO1t5J5SQka7jijcCWiobW5ju7ZLiLOxxkZGCPrWbe+KNJsNYi0q4uCtzLjA2EqpP3QT0GapQk3ZIDVlV2jdY22uVIVsZwfWsxvD9p/Z6wRoiTqBtuAg3bhzu/OtWg0RnKOzAxlkuotQEt4bhYnn2RlZF2egyvXB+tVvGd7bWGlR3LSLFeLKBZuWAZXPU+646juKr3F6t3qL2vhyH7ZcRyFpZpJD9ktn7k4+8/8Asr+OK09N8O29nM17eStqOoyLtkupwM4P8KL0RfYfjmqlKLadhGNpTXXjWGR9Quo4tPhk8p7O0Yjz2ABJkbrt5+6PxJrrYIIbaFIIIkiijG1ERQFUegArm9Z1bT/C+vW1xM/lQ3kJjmjjTO3Z918DsMkfl6V00brIiyIwZWGVI6EUpJ/Fayewx1FFFQAlLRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRSUtABWXrHnXEttZW4Xc7+a5cHbtXnBx6nFalJiqjLldwMnTGmsrm7tbvYAf9IRkBCAH7w59Dz+NZ974d03xJLHrduZIbxCDHI3KsUPy707jj2OK3b+1e7hWNJhEN4ZspuDAdiPSuctNZvQJdL0iKPUL1Jn8yY/Lb22WJ+dh9499q8+uK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7. Join A9 with B.
![](data:image/jpeg;base64,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8. As we have to divide in 2:3:4, we draw a line from A2 and A5 parallel to A9B.
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9. The point where it cuts AB is P and Q
Here, AP : PQ : QB = 2 : 3 : 5
Question 3.Construct the following with the help of straight-edge and compass only:
Construct a triangle with sides 4 cm, 5 cm, 7 cm and then construct a triangle similar to it whose sides have lengths in the ratio 2 : 3 to the lengths of the corresponding sides of the first triangle.
Answer:Steps of Construction:
1.Draw triangle ABC of given dimensions.
![](data:image/jpeg;base64,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)
2. Draw a ray AX making an acute angle with AB.
![](data:image/jpeg;base64,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)
3. We have to construct triangle having ratio of 2:3. So we make 3 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A3.
![](data:image/jpeg;base64,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)
7. Join A3 with B.
8. As we have to divide in 2:3, we draw a line from A2 parallel to A3B.
![](data:image/jpeg;base64,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)
9. The point where it cuts AB is P.
10. From P, draw a line parallel to BC.
![](data:image/jpeg;base64,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)
11. APQ is the required triangle.
Question 4.Construct the following with the help of straight-edge and compass only:
Draw ΔPQR with m∠P = 60, m∠Q = 45 and PQ = 6 cm. Then construct ΔPBC whose sides have lengths
times the lengths of the corresponding sides of ΔPQR.
Answer:Steps of Construction:
1. Draw triangle PQR of given dimensions.
![](data:image/jpeg;base64,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)
3. Draw a ray PX making an acute angle with PQ.
![](data:image/jpeg;base64,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)
3. We have to construct triangle having ratio of 5:3. So we make 5 equal arcs on ray PX.
4. Taking P as center, cut an arc on ray PX. Mark the point as P1.
5. Now, with the same radius cut an arc on PX with P1 as center.
6. Mark till P5.
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7. Join P3 with Q.Extend PQ.
8. As we have to divide in 5:3, we draw a line from P5 parallel to P3Q.
9. The point where it cuts extended PQ is S.
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10. From S, draw a line parallel to QR.
11. PST is the required triangle.
![](data:image/jpeg;base64,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)
Question 5.Construct the following with the help of straight-edge and compass only:
Draw ΔABC having m
ABC = 90, BC = 4 cm and AC = 5 cm. Then construct ΔBXY, where scale factor is
.
Answer:Steps of Construction:
1. Draw triangle ABC of given dimensions.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACIAKMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2WqVrqkd1fz2ioymL7rnpJg4bH0PFT3sskFnNLFG0kioSiKMkntWMNNvdOisrgTG4a3b540iwSH+/z35OfwrWEYtO/wAhM6CikFLWQwooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApKWkoA5bRPGD6nrbafPbxwBw5iG/51KnowPf6eldVXPw6daX+ra5DcQKytLCcjhgfLGCCOQfepBeXehnZqTtc2PRL3HzR+0oH/AKEPxx1qpuLfuqwG5RTUdZEV0YMrDIYHIIp1SAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBkaZ/yHta/66xf+ilrWIDAggEHqDWTpn/Ie1r/rrF/6KWtegDEfT7rR3afR1822JzJYE4HuYj/Cf9nofatHT9RttSgMtu5O07XRhteNv7rA8g1arN1DSBcTi9tJTaXyjAmUZDj+64/iX9R2oA0qKy7HV2e4FhqEQtL7GQmcpMPWNu/06itSgAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAMjTP+Q9rX/XWL/0Uta9ZGmf8h7Wv+usX/opa16ACiiigCtfWFtqNuYLqIOmcg5wVPYg9QfcVmi9vNDPl6m7XNj0S+A+aP2lA/wDQhx64rbpCAwIIBB6g96AER1kQOjBlYZBByCKdWI+n3WjO0+kL5tsTmSwJwB6mI/wn/Z6H2rRsNRttShMtu5O07XRhteNu6sOoNAFqiiigAooooAKKKKACiiigAooooAKKKKACiiigDI0z/kPa1/11i/8ARS1r1kaZ/wAh7Wv+usX/AKKWtegAooooAKKKKACs2/0gXE4vbOY2l+owJlGQ4/uuv8Q/UdjWlRQBmWOrmS4FhqEQtL4DITOUmH96Nu49uorTqtfafbajbmC6jDpnIOcMp7FT1B9xWaL270MiPU3a5seiXwHzR+0oH/oQ49cUAbdFNR1dQyMGVhkEHIIp1ABRRRQAUUUUAFFFFABRRRQAUUUUAZGmf8h7Wv8ArrF/6KWtesjTP+Q9rX/XWL/0UtarMqjLMAPUnFADqKaXCjLEADuTQWC4yQMnAz3oAdRRRQAUUUUAFIQGBBAIPUHvS0UAYjafdaMxm0hfNtScyWBOAPUxH+E/7PQ+1aNhqNtqUHm2zk7TtdGGGjburA8g1arNv9IE8/22zlNpfKMCZRkOP7rr/EP1HY0AaVFZljq5kuBYahD9kvgMhM5SUD+KNu49uo71p0AFFFFABRRRQAUUUUAFFFFAGRpn/Ie1r/rrF/6KWqev2wk1ixmvLGW/sEikUwxJv2yEjaxTuMZGexNNt9Qng8R63HDYvcBZIdzLIq4/dD1qaVItav4oLu0urKeKNnimiuNrbcgMMqeh44qJa6Gc7NWMPQ4/7VubCw1GEyWsK3bRwTNvB2yhFB9dqkjvV7S9LfVNLRTcFUtLi4t4y67z5YkwpUk8MAoAbnitmbw9p8trbW6JJbra58h4JCjpnrhhzz39au2dnBYWkdrbRiOGIYVev+TUxg1uTGm1uTCloorU2CiiigAooooAKKKKAK1/p9tqNuYLqPeucqQcMh7FT1B9xWaL270NhHqjm4suiXwHMfoJQP8A0IceuK26RlDKVYAgjBBHWgBFZXUMrBlYZBByCKdWI1hdaKzTaQvnWpOZLAnGPUxE9D/sng+1aNhqNtqUHnW0mdp2ujDDRt3VgeQaALVNDKSV3AkdRmqurzS2+k3U0JxIkZKkdveqv9madBbwThhCyFWFwGwzE+p75/rVqKauwNaikoqAFpKoa9eTWGiXV1AyrJEmVZhkDkckVnadq00urxWa6nbalHJGzO0MYUw4xgnBIIPStY0pSjzIVznNL8Y6c3iTV5JY544ruRWhZYmkJEahDlVBI6ZrZt/EemvrSTBrny1tmUsbSUcllIH3fY10FtpdhaXM11bWcMM85zLIiAM/1NW6ipyOV4KyFymT/wAJPpX/AD1n/wDAWX/4mj/hJ9K/56z/APgLL/8AE1rUVJRk/wDCT6V/z1n/APAWX/4mj/hJ9K/56z/+Asv/AMTWtRQBk/8ACT6V/wA9Z/8AwFl/+Jo/4SfSv+es/wD4Cy//ABNa1FAGT/wk+lf89Z//AAFl/wDiaP8AhJ9K/wCes/8A4Cy//E1rUUAZP/CT6V/z1n/8BZf/AImj/hJ9K/56z/8AgLL/APE1rUUAZP8Awk+lf89Z/wDwFl/+Jo/4SfSv+es//gLL/wDE1rUUAZP/AAk+lf8APWf/AMBZf/iazb/UNJnn+22d1PaXyjAmW0lKyD+667fmH6jsa6iigDlNL8aR6lfR6fcWLRmV2hLhsqXAOflIBCnB68+1bcejWUciMFcrGdyRtIxRD6hTxUy6bZLfm/FrELojBm2jdj61arRzS+DQQlFLRWYyhrVnLqGkXNpCUEki4XecDOQeappp+oXWp2l1dQ2lslqWYeQxZnJUjBOBgc5/AUUVpGpKK5V/VxWNqloorMYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB//9k=)
2. Draw a ray BX making an acute angle with BC .
![](data:image/jpeg;base64,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)
3. We have to construct triangle having ratio of 4:3. So we make 4 equal arcs on ray BX.
4. Taking B as center, cut an arc on ray BX. Mark the point as B1.
5. Now, with the same radius cut an arc on BX with B1 as center.
6. Mark till B4.
![](data:image/jpeg;base64,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)
7. Join B3 with C. Extend BC.
8. As we have to divide in 4:3, we draw a line from B4 parallel to B3C.
9. The point where it cuts extended BC is P.
![](data:image/jpeg;base64,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)
10. From P, draw a line parallel to AC.
11. BPQ is the required triangle.
![](data:image/jpeg;base64,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)
Question 6.Construct the following with the help of straight-edge and compass only:
Draw
of length 6.5 cm and divide it in the ratio 4 : 7. Measure the two parts.
Answer:Steps of Construction:
1. Draw a line PQ of length 6.5cm
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS0AAAAbCAIAAACm1U69AAAAAXNSR0IArs4c6QAADC5JREFUeF7tnHtsVFUex8+5j3l22mmnXbBCAVsoS4ESXaA8QkGDi0LksRhKNCwK8QUJYRFj2BB0NUGTVfQPE3ZDslkFjMZFHtviwirEEqBkedWFhdptEQVqn9PO+77Ofs+9MDbVMGV0FrX3ppncufee+/id8+nv8T13KGOM2IttAdsCt9UCwm29un1x2wK2BbgFbA7tcWBb4PZbIH0ODcOwYlo7sr393WjfQcYsgOGt6zo+rQGPz0xciqZNERpSSjNxT/Y5bQv8SCwA6gThG19lwZKJYZ++P8TdhEI9qqb8SExm34ZtgR/cAiaELBwJqSof55kg0LpnygyOuEGtTBE+tw+ZBjMEym/GOlwxvaB05Vrbh7uPXvki4fd75jxYVj5+mBmgYlf6YP/gRrRPaFsgPQtg0FMOHW1r697398OtbQmH7J42pWRixTCKQU7cJgt8yFtUpHeV3q0o0wwisLBOTtSFjRgTAZMhEUGnkppf4Bk23OPJSuA6VHficoyqjNBIVPn9hh0n6nwuoVRTOu4Y1vjyqw+UlnAU7cW2wM/CAiockqbTVzfvPHdOz/KVJ6IJUTi5+ncT754wnoAFLKLltyzXZaGIdZBpfb01OCnTFSbEglHvhjVdWsjt8oR1zQsODaGbGVLRcP+iR5yjR+LfgwQK+YVE8vGhui2bm6g0V5azZao3X36/ovLLiskFhoKGeABbkPxZDMWB+xAIRgUmxC9/0X2u3lFSvITKedh08d81M2azx347R5ZEQk3kGFg0RzvFpwVhEr9boxFxqcpovCPqXrdCGTde+s2jQkIRcDJDY5/V9+zd1VY+MeuJpwpyPPy8hkoF2di1p/qdP0mGNMsgLrdotHxd4/EfLClRBOaww9KBO3p/Nk/OJKa5qSPYdKk11zuv+K4qQ3QIImm8ePieKeEnV85xOyVCEtwjMTinpPNLQmgBiU9gBFD75Rh5fsio1hkR1z8Vm1oZX7nSw4iDOz4mxTXy/vbOj/8Z3fjiHSUl4NAghshotPly43Nrjrd1TstyDTf0zlCs5sWXK++dVaobXZT4bE0yvQFp1Z+TVWhU6niC0muLdVqrdG7tEkUeGyU3WuuZqyWk91w/xVYGiwtisLVV/cOmQxKr8AWG6KSrsXHvssfGz39ghskYyjYyMjqD6bwjOG+cQ7hIXmvhySWO0U0WrvfRze0ADg1GWVdEeO6JWMUMeeWTaIbYUiO6m4i0Zo/2l23xFzZ7ysbijCoxJJ0poqhUH7j4zjvHjUS+rgbnzB2+7NF7HU6ZsRgV3HZYmvbI+06EknwmkcNK72K6xSHaQub69q60b2bANgREoIsIcYE4a2svfvjhybhOdC18d/kdVUsrc3x+0zKKQRw6Z05XVDnYqamqIcuCL9vhQxHnevkmmT2mLl7yuBTIBqPkuac6pk73L38SPtdCWe4JG39+K3yhSdmwMfuuIQ5C4giIdU3WhIQkCleutFz56lqePzByZBGlCmEy0xyC3E8/PGB7+WYPHo/HP/roo0OHDmFlwoQJ8+fPLyws7KPTWs5w165dBw8eVFX0HV+A5ZIlS2bNmoUV2x9+z7EFn4bapYhwkumCIF69du2/l770Z+f+cmSxJKtMl6kgIns0iKwaYlNj/Hx9uP2apGuSICr+XDK6VC8bm+9w8/Yob96ITlPcFDhUUH8JxsS1T3QUDvZOu0/V4GqJpsddjf8RT5/++v6FvqqHAy4ZTPN/t4yHpsRgiiSAzOsLTgLFgjHJzg/THgShUOi111577733xowZ43A4zp49O3bs2Ndff33IkCG91WQLy4ceeuj48eMTJ060fCC2rFixYvHixX1057RvZoA3RALGQ0szCYBKd8MagBClE4FQFR8JzVFXx47WtuXnKaNLAnl57khMafi8o+WreMnoX1T+2p2NqiVQ4dGlzE920wX1Up0JentEWr+qJx4F0AlDz6a0R2CSQ3RMr/TMfFAs8CNYTe1bB3jnfc/H37t375o1azZs2ADPJknSgQMH8HXTpk2PP/44YEumgrhKJBKZMmUKqFu7di2+gj0sbrfb6eT1dNsffs+O+M7mjGjwkwKTwSZCVkKcDQ2xv+3qKirKvX+2K5ALH4k9QjiqH6tVTtSFJs0S76sMiLxYoxPkj6kWcGgwgbSHyfrVbRMmZD/8iMOAO6REpiTLS1wu8B8RiCzQb7xfqnPa+2/ZArFYbNWqVeFw+N1337WQQ8x57NixwYMHFxcX8+kRvWZXNTY2zpw58+23354+fToO83q91vXsmYa3bPd+N0D5hSuDQIXojMSVhHd/ddely8HFSwrvLHQSAxo7PJ7EKOQGtv2v4Ug8VPVIYFAAu8AtYpYUhdPrKgeqO6Kge7LUOwvo0MH60EF0UAH1ehDzKqLhocyGsN89ltaB3d3d58+fnzFjRkdHx549e7Zv337mzJmKiopRo0aBwD5zi8+dO4ctOP6ZZ55ZuHDhxo0bscXiMO3Zwmnd9YBqdEOsp4hUxVCPfqmZFg0N5OZJKNWYqSAPGCnVHM54WZkr2pN99bJZZ+GKempZH401pHsi4l5dpwyqiCl6GObkGVRfqIK8z876MjTiktgg1IQzBFqA6o/msmzZsjfffBN+EpfuHZTi64kTJ9ra2lCn8fv948aN2717N5LD+vp6C8UM3ap92l4VSDGu6N09LCcn2+PkigWlqE8ijeSsIn0sKBCVhNDd5TJlRgSxqXM6tNJ4Kon+00WgbpobsSj4xiYntESelZoVGnvJhAUschBetre3f/LJJ2VlZdu2bfvggw+WLl2KIk1NTc23873y8vL169e/8cYbwBWlnZ07dwLLLVu22MXSTHSQdU7ulriOwP8rgisd9UqqChQpHMfQ2s2LMkCOQUyAf1QhdphaPyBKvZjqPNHQMtsne908/kQ+iqwUHpFhtqkBsVJChJv6TPYRaVnAwgweLxqNTpo06emnny4tLS0pKVm9ejWYBIeJRKI3iuB2wYIFqN+MGDEC9RsEqHCJs2fPPnLkSGdnp12kSasT+tMIPuq6LIiXEWWH4PKyaCSuJeCxAJwCP3Zj5gwNdugOmXlzoPU7wCHUB5Oymy3wh/Cebp+HvrA5b8HiLBN9/AFMCikKcpTApZR+zc3pz9PYx/S2QBIbVDsLCgqAnyzL1vumPp8PQHZ1dSkKf+Omz3uo1mHWbBvszc/PB8Yg1jZvxiyAZM0qe4I3NcsrjSh0Xm6OdfXwKWx4O0KPCt2dLKFhog1t+DyY41GHDrKc2g2kUnDIfR2IIzl+we25EZfaDjBj/fmdJ87KyioqKkIh1BIAARigunr1KrZbyaFVMrW2P/vss6+88or11drb0NAAxT83N/f/e9cD72oWVIxBShgz1tXZI9Wd1LqRAFJXR1Dfs6+l5h+ho0fUL79wDC/OHVSIrolg6ps5HTyFJ7MDzh/FYMrJyVm0aNHhw4cxUUbTNNC4f//+06dPY4qMx+NB/NnU1ATYsIKvKOps3boV1RpwiIPR5NNPP62qqnK5ENrYS4YsgETNqpKgpCkZRC8e5bq7wnOqvm3//tCZ80Zb2KDOrJN1zgPVeFvDPe5XkiAgoXNBdCQUxbYUcWn6v4uRoccdsKdtaWl5/vnnjx49OnnyZOj4tbW1yPpeeuklxJyAbfny5Sio7tixA2rhhQsXIDa2trZOnToVM+DQBIIHijoIZfkw6aU0DlhjZuDBTXGC10qgCKpmUi+E4+KZs9GGs1qoU3Q4oTdostOZG3C3Xu0pvFO7p8I5fKjHrH1CvUA19WYu0eYwA11266e0JHiIh/v27QNXAA9K/dy5cwOBgKUKoi4K5NatWwd/iNM3NzdXV1efOnUKieK0adPmzZuXl5dnyYw2h7du/v60QCKe/LUKwAg1n1duMBktHJS62pmqakgRvD7q8stfNSuf/St4VymdXJHP6UVimSrutDnsTx9k/BiQBvYAFa6EigtYsoLM5MsWgBCYYSNwxQocJvZCXcRX60irutNHacz4fQ+kC5glF+vdQjNj5ytR8xVEl4kZvl5/GREdEYtiEhxzekTI7+ZLUlAibH/4UxguvX8LLCnH93n/sI9M30elsP1h5vrZhAwCIRQILBJ+pcb832f+ZKEQx8xSkMaFBqoaGjQGlLJRnoH2DqlBRzKJmaE35/B/bEGVeh7m/vgAAAAASUVORK5CYII=)
2.Draw a ray PX making an acute angle with PQ.
![](data:image/jpeg;base64,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)
3. We have to divide line in ratio of 4:7. So we make 4+7 =11 equal arcs on ray PX.
4. Taking P as center, cut an arc on ray PX. Mark the point as P1.
5. Now, with the same radius cut an arc on PX with P1 as center.
6. Mark till P11.
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)
7. Join P11 with Q.
8. As we have to divide in 4:7, we draw a line from P4 parallel to P11Q.
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9. The point where it cuts PQ is A.
Construct the following with the help of straight-edge and compass only:
Draw of length 7.4 cm and divide it in the ratio 5 : 7.
Answer:
Steps of Construction:
1. Draw a line AB of length 7.4cm
2.Draw a ray AX making an acute angle with AB.
3. We have to divide line in ratio of 5:7. So we make 5+7 =12 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A12.
7. Join A12 with B.
8. As we have to divide in 5:7, we draw a line from A5 parallel to A11B.
9. The point where it cuts AB is P.
Question 2.
Construct the following with the help of straight-edge and compass only:
Divide a line-segment into three parts in the ratio 2 : 3 : 4 in the same order.
Answer:
Steps of Construction:
1. Draw a line AB of any length.
2.Draw a ray AX making an acute angle with AB.
3. We have to divide line in ratio of 2:3:4. So we make 2+3+4 =9 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A9.
7. Join A9 with B.
8. As we have to divide in 2:3:4, we draw a line from A2 and A5 parallel to A9B.
9. The point where it cuts AB is P and Q
Here, AP : PQ : QB = 2 : 3 : 5
Question 3.
Construct the following with the help of straight-edge and compass only:
Construct a triangle with sides 4 cm, 5 cm, 7 cm and then construct a triangle similar to it whose sides have lengths in the ratio 2 : 3 to the lengths of the corresponding sides of the first triangle.
Answer:
Steps of Construction:
1.Draw triangle ABC of given dimensions.
2. Draw a ray AX making an acute angle with AB.
3. We have to construct triangle having ratio of 2:3. So we make 3 equal arcs on ray AX.
4. Taking A as center, cut an arc on ray AX. Mark the point as A1.
5. Now, with the same radius cut an arc on AX with A1 as center.
6. Mark till A3.
7. Join A3 with B.
8. As we have to divide in 2:3, we draw a line from A2 parallel to A3B.
9. The point where it cuts AB is P.
10. From P, draw a line parallel to BC.
11. APQ is the required triangle.
Question 4.
Construct the following with the help of straight-edge and compass only:
Draw ΔPQR with m∠P = 60, m∠Q = 45 and PQ = 6 cm. Then construct ΔPBC whose sides have lengths times the lengths of the corresponding sides of ΔPQR.
Answer:
Steps of Construction:
1. Draw triangle PQR of given dimensions.
3. Draw a ray PX making an acute angle with PQ.
3. We have to construct triangle having ratio of 5:3. So we make 5 equal arcs on ray PX.
4. Taking P as center, cut an arc on ray PX. Mark the point as P1.
5. Now, with the same radius cut an arc on PX with P1 as center.
6. Mark till P5.
7. Join P3 with Q.Extend PQ.
8. As we have to divide in 5:3, we draw a line from P5 parallel to P3Q.
9. The point where it cuts extended PQ is S.
10. From S, draw a line parallel to QR.
11. PST is the required triangle.
Question 5.
Construct the following with the help of straight-edge and compass only:
Draw ΔABC having mABC = 90, BC = 4 cm and AC = 5 cm. Then construct ΔBXY, where scale factor is
.
Answer:
Steps of Construction:
1. Draw triangle ABC of given dimensions.
2. Draw a ray BX making an acute angle with BC .
3. We have to construct triangle having ratio of 4:3. So we make 4 equal arcs on ray BX.
4. Taking B as center, cut an arc on ray BX. Mark the point as B1.
5. Now, with the same radius cut an arc on BX with B1 as center.
6. Mark till B4.
7. Join B3 with C. Extend BC.
8. As we have to divide in 4:3, we draw a line from B4 parallel to B3C.
9. The point where it cuts extended BC is P.
10. From P, draw a line parallel to AC.
11. BPQ is the required triangle.
Question 6.
Construct the following with the help of straight-edge and compass only:
Draw of length 6.5 cm and divide it in the ratio 4 : 7. Measure the two parts.
Answer:
Steps of Construction:
1. Draw a line PQ of length 6.5cm
2.Draw a ray PX making an acute angle with PQ.
3. We have to divide line in ratio of 4:7. So we make 4+7 =11 equal arcs on ray PX.
4. Taking P as center, cut an arc on ray PX. Mark the point as P1.
5. Now, with the same radius cut an arc on PX with P1 as center.
6. Mark till P11.
7. Join P11 with Q.
8. As we have to divide in 4:7, we draw a line from P4 parallel to P11Q.
9. The point where it cuts PQ is A.
Exercise 12
Question 1.Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct two tangents to the circle from this point. Measure them.
Answer:Steps of Construction:
1. Draw a circle of radius 5cm and center O.
2. Draw a line OP such that OP= 8cm
![](data:image/jpeg;base64,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)
3. Draw a perpendicular bisector of OP which cuts OP at M.
![](data:image/jpeg;base64,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)
4. Taking M as center and radius OM, draw a circle.
5. The two circles intersect at A and B.
![](data:image/jpeg;base64,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)
6. Join AP and BP. AB and BP are the required tangents.
![](data:image/jpeg;base64,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)
Question 2.Draw ⨀ (O, 4). Construct a pair of tangents from A where OA = 10 units.
Answer:Steps of Construction:
1. Draw a circle of radius 4cm and center O.
2. Draw a line OA such that OA= 10cm
![](data:image/jpeg;base64,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)
3. Draw a perpendicular bisector of OA which cuts OA at M.
![](data:image/jpeg;base64,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)
4. Taking M as center and radius OM, draw a circle.
5. The two circles intersect at P and Q.
![](data:image/jpeg;base64,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)
6. Join AP and AQ. AP and AQ are the required tangents.
![](data:image/jpeg;base64,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)
Question 3.Draw a circle with the help of a circular bangle. Construct two tangents to this circle through a point in the exterior of the circle.
Answer:Steps of construction:
1. Draw a circle(Say C1) with the help of a bangle, and take any three points A, B and C on its circumference
![](data:image/jpeg;base64,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)
2. Join AB and BC and draw the perpendicular bisector of AB and BC which intersect each other at O.
![](data:image/jpeg;base64,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)
3. O is the center of circle, now take any point P outside the circle and join OP.
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)
4. Draw the perpendicular bisector of OP, which intersect OP at O'.
![](data:image/jpeg;base64,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)
5. Taking O' as center and O'O = O'P as radius, draw a circle C2, which intersects the previous circle at Q and R.
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6. Join PQ and PR, which are required tangents.
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)
Question 4.Draw ⨀(O, r).
is a diameter of 0(0, r) . Points A and B are on the
such that A—P—Q and P—Q—B. Construct tangents through A and B to ⨀(O, r) .
Answer:Steps of Construction:
1. Draw a circle of any radius(r ) and center O. Draw a diameter PQ of this circle.
2. Extend PQ both the sides as APQB is a straight line.
![](data:image/jpeg;base64,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)
3. Draw a perpendicular bisector of OA and OB which cuts OA and OB.
![](data:image/jpeg;base64,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)
4. Taking OA and OB as diameters, draw two circles.
![](data:image/jpeg;base64,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)
5. The three circles intersect at K,L and M,N.
6. Join AK and AL. Join BM and BN.
![](data:image/jpeg;base64,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)
7. AK,AL,BM and BN are the required tangents.
Question 5.Draw AB such that AB = 10 cm. Draw ⨀(A, 3) and ⨀(B, 4). Construct tangents to each circle through the centre of the other circle.
Answer:Steps of Construction:
1. Draw a circle of any radius 3 and center A.
2. With A as center, draw a circle of radius 3 cm. With B as center, draw a circle of radius 4cm.
![](data:image/jpeg;base64,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)
3. Draw a perpendicular bisector of AB which cuts AB at M.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACoATcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAM++/5Cum/wC/J/6Aa0Kz77/kK6b/AL8n/oBrQoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAM++/5Cum/wC/J/6Aa0Kz77/kK6b/AL8n/oBrQoAKKKKACiiigAprukaF5GCqoyWY4Aqlc6iRObSyi+03I+8M4SL3du306n0psekiZxNqUv2yUHIVhiJP91P6nJoADq4nyNPtpbz/AKaL8kf/AH2ev4Zo8rV5/v3NvaD+7FGZG/76bA/StDpS0AZ/9lO5zNqd9IT1xIEH/joFH9jW/wDz2vCfX7XJ/wDFVoUUAZx0gD/V39/H9Jy3/oWaPsuqQ5MOopMP7txCP5rj+VaNFAGd/aNzbf8AH9YSIo6y2581PqQAGH5Vct7qC7iEtvMkqH+JGzUtUrnS4J5TcRlra5/57QnDH69mHsQaALtFZi389iwi1RVCE4S7jGIz/vD+A/p79q0qAFooooAKKKKACiiigAooqld6h5UwtbWP7RdkZ8sHCoP7znsP1PYUAW5JEiRpJHVEUZLMcAfjVD+1xPxYWs13/wBNFGyP/vpuv4Zoj0oSuJ9Rk+1zA5CkYij/AN1P6nJrRoAz8azKetlbKe2GlI/9BpDaaoT/AMhVB9LUf41o0UAZ/k6xGPkvLWb2kgK/qG/pSG9vrf8A4+tOZ1HV7V/M/wDHTg/lmtGigCva39rehvs8yuV+8vRl+qnkfjViqt3p1tekNKm2VfuSodrp9GHP9Kq/a7nSzt1BvOtegu1XBT/roB/6EOPUCgDUopAQwBBBB6EUtABRRRQAUUUUAZ99/wAhXTf9+T/0A1oVn33/ACFdN/35P/QDWhQAUUUUAFZk9xNqE72dk5jjjO2e5X+E/wBxP9r1Pb69H308s9wNOtHKSMu6aVesKe3+0eQPxPardvbxWsCQQoEjQYVR2oAS1tYbOAQ28YRB2Hc9yT3PvU1FFABRRRQAUUUUAFFFFABRRRQA1lV1KOoZWGCCMgissrJoZ3Juk03+JerW3uPVPbt9OmtRQAisrqGVgysMgg5BFLWXGP7Hulh/5cbhsR/9MHP8P+6e3oeO4rUoAKKKKACiioLy5SztZLiQEhB90dWPYD3JwPxoAgvrqUSLZ2mDcyjO4jIiXux/oO5/GprOyisoTHHkljud2OWkbuSe5qPTrV7eJpbjDXU53zMPXso9gOB+ferlABRRRQAUUUUAFFFFABSEAggjIPUUtFAGUB/YkgC/8g52xj/n3J9P9g/p9OmrTXRZEaN1DIwwykZBHpVDTma2mk02VixiG6Bicl4+34qePyPegDRooooAKKKKAM++/wCQrpv+/J/6Aa0Kz77/AJCum/78n/oBrQoAKr3t0tlaSXDKW2j5UHV2PAUe5JAqxWdL/pmsxw9YrNfNf3kbIUfgMn8RQBNp1o1rbkzEPcTN5k7jux9PYcAewq3RRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBFc28V3byW8y7o5F2sKraZPKySWty264tW2O398fwv+I/UGr1Z1/8A6LfW1+vCkiCb/dY/KfwbH/fRoA0aKKKACs64/wBL1eC26x2y+fJ7schB/wChH8BWjWfpf72S9ujjMtwyg/7KfJ/MH86ANCiiigAooooAKKKKACiq1nf29+sjW7FhHIY2yMcj+nvVmm007MAooopAFZ2rjyY4tQX71o+5sd4zw4/Ln/gIrRpksazRPG4yrqVYeoNADutLVHRpGk0m338vGvlt9VJU/wAqvUAFFFFAGfff8hXTf9+T/wBANaFZerTpa3dlcS58uHzXbAycCMk8VMmsWUktjGkhZr9DJAAp5UDJz6cGgC7VDRsyWr3jZ3XcrS8/3ei/+Ohal1WYwaTdSrwyxNt5xzjj9amtoRb2sUC9I0CD8BigCWiiigAooooAKKKKACiio550toHmkzsRSxwM0bgSUVXt7uO5Z0VZEdMblkXaRnoasU2mtwCiiikAUUUUAFQXtst5ZTWzcCVCufQ9jU9FAFXTbk3enQTt990G8ejdCPzzRUOlZT7ZBxiK6fAHYNh//ZqKANCs/Q8nR4GJyX3N+bE/1rQrP0LI0iFD1Quh/BiP6UAaFFFFABRRRQAVla3rVlpkaW9xex2s90GWBpAdoPqT2AJHWtWq1zp9neSwy3NrFNJA26JnQEofUVUWk9QMXT7jR9Mut0OvWskLQrGyyXKE5X7pH4E/pWn/AG/ov/QWsv8AwIT/ABq55MX/ADyT/vkUeTF/zyT/AL5FEpOTuwKf9v6L/wBBay/8CE/xo/t/Rf8AoLWX/gQn+NXPJi/55J/3yKPJi/55J/3yKkCn/b+i/wDQWsv/AAIT/Gj+39F/6C1l/wCBCf41c8mL/nkn/fIo8mL/AJ5J/wB8igDI0nV9MWO6X+0rVl+1SFT5y9zn196v/wBsaZ/0EbX/AL/L/jUOkxq0d05iUBrqXHA6A7f6Vf8AKj/55r+VAFb+2NM/6CNr/wB/l/xo/tjTP+gja/8Af5f8as+VH/zzX8qPKj/55r+VAHM+Idb0iS7s7H+1LZZblZkU78qu5CoJI6ckU60hsLbUYrk6vZNHDKxiUSjKxlW+Xr/eYn6AVoajY2kutaTLJaxPJG8mxmQEr8h6VqeVH/zzX8qAMfWtW0t9LkU6hakM8YP75ehdc96t/wBv6N/0FrL/AMCE/wAabraRppUrmNcIyMfl7B1NXvJi/wCeSf8AfIoAp/2/ov8A0FrL/wACE/xo/t/Rf+gtZf8AgQn+NXPJi/55J/3yKPJi/wCeSf8AfIoAp/2/ov8A0FrL/wACE/xo/t/Rf+gtZf8AgQn+NXPJi/55J/3yKPJi/wCeSf8AfIoAp/2/ov8A0FrL/wACE/xo/t/Rf+gtZf8AgQn+NXPJi/55J/3yKPJi/wCeSf8AfIoAp/2/ov8A0FrL/wACE/xqpea3pN8DpkGoQST3SlE2NvUE9ASOBmtfyYv+eSf98ion06ykuYrprWIzxfck2DK/Sqi0ndgQ6fYvaSyuwjQSBR5cZJGRnnJ7/wCFX6KKTbk7sAooopAFFFFABRRRQBn2XGq6kP8AbjP/AI4P8KKLLnVNSbtvjX8dgP8AWigDQrP0391c31qf4J/MXj+Fxu/9C3flWhWdeH7Jqdte9I5f9HlPpk5Q/wDfWR/wKgDRooooAKKKKACiiigAooooAKKKKACo55kt7eSeQ4SNCzfQDNSVnaqftLwaavP2ht0vtEpBb8zhfxoAl0iFoNKt0cYcpvcf7TfMf1Jq5RRQAUUUUAZ99/yFdN/35P8A0A1oVn33/IV03/fk/wDQDWhQBV1KE3GmXUK53PEwXHrjj9aktJxc2cFwOksav+YzU1Z+j/uYZrI9bWZkA/2D8y/oQPwoA0KKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiq2oXP2OwnuMZZEJUerdh+JwKAINJJkS6uM5E11IVOOynYP/QaKsWFt9jsILfqY0Ck+p7n86KALFRXNvHd20lvMu6ORSrCpaKAKOm3MjB7O6bN1b4Dn/nov8Lj6/oQRV6qd9ZNOUuLdxFdw58tyOCD1VvVT+nB7UtlfJdhkZDDcRcSwsfmQ/wBQex70AW6KKKACiiigAooooAKKKZLLHDE0srqiIMszHAAoASeeK2geeZwkca7mY9hVTTYZXaTULlCk1xjajdYox91frySfc+1RRo+rzJcTIyWUbboYmGDKw6Ow7Adh+J7VqUAFFFFABRRRQBn33/IV03/fk/8AQDWhWfff8hXTf9+T/wBANaFABWdc/wCh6tDddIrkC3l9m6ofzJX8RWjUN3bR3lrJby52SLg46j3HuOtAE1FUtNupJo3t7kj7VbHZLj+L0cexHP5jtV2gAooooAKKKKACiiigAooooAKKKKACiiigArOuz9s1S3s15SDFxN+H3B+eT/wGrV5dR2Vq9xLkqo4UdWJ4AHuTxUWm2skELSXGDc3DeZMR0B7KPYDA/CgC5RRRQAUUUUAFVLzT47srKrtDcR/6ueP7y+3uPY8VbooAzRqM1l8mqRbFHS5iBMZ/3h1T8ePetCOSOVBJG6ujDIZTkH8adVB9HtC7SW/mWkjHJa3fZn6jofxFAF+is8W2qRZ8vUIph2E8HP5qR/KkzrY/gsD77nH9KANGis8JrL8NPZw/7sTOf1IpP7Jab/j+vrm5B6oG8tD+C4z+JNAD7jVYIpTbwhrq4H/LGHkj/ePRfxNRpYTXcqz6myttO6O2TmND2J/vH3PA7DvV2C3htYhFbxJFGOiooAqWgAooooAKKKKACiiigDPvv+Qrpv8Avyf+gGtCs++/5Cum/wC/J/6Aa0KACiiigCjf2svmJfWYBuYRgoTgTJ3Qn9Qex+pqe0u4r23WaEkqeCCMFSOoI7EelT1n3NnNDcNfWAHmt/rYScLMB/JvQ/gfYA0KKr2d9DexloiQyHbJG4w8Z9GHarFABRRRQAUUUUAFFFFABRRRQAU13WNGd2CqoySTgAU2eeK2haaeRY40GWZjgCs8RS6w4kuY2isVOUgYYaY9i47L6L37+lAC2ytql0l9IpFrEc2qMMbz/wA9CP8A0H2578adFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBn33/IV03/fk/wDQDWhWfff8hXTf9+T/ANANaFABRRRQAUUUUAU7vTo7mQTxu1vcqMLPH1x6EdGHsahGoz2Xy6nDtUf8vMILRn6jqn45HvWlRQAyKWOaMSRSLIjdGU5B/Gn1Rk0m1aQyw77WUnJe3bZn6jofxBpvlatD/q7m3uR6TIUb814/SgDQoqh9r1Bfv6WW94p1b+eKd/aE3/QMu/8AyH/8VQBdoqib29b/AFelyj/rpKi/yJpP+JvMf+XS1U+m6Vh/6CKALxOBk8CqD6skrmLT4jeSg4JQ4jX/AHn6fgMn2o/siOU7r2eW8P8AdlOE/wC+BgfnmryIsaBEUKoGAAMAUAUYdOaSZbrUJRcTIcogGI4j/sjuf9o8/StCiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAM++/5Cum/78n/oBrQoooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAP//Z)
4. With M as center and AM as radius, draw a circle.
5. The three circles intersect at K,L and M,N.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCAC/AUUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAooooAKKKKACiiq93f21iitcShSxwigEs59AByfwoAsU1mVFLMwVR1JOAKzxLql7/qo1sIT/HMN8p+ijhfxJ+lPXRrUsHut95IP4rhtw/Bfuj8BQANrVjuKRStcOP4YEMn8hikGo3Ui5h0q5Pp5rIn9c/pV9VVFCqoVR0AGAKWgDPFzqx6aZCo/2rr/AAWqGiXGqro9tt0+B12nkXRB6n/ZrfrP0H/kC23+6f5mgAF9fKCZdKl4/wCeUqN/Mij+2rVADcpPa84/fwso/Pp+taFFAEcM8Nwm+GVJV/vIwI/SpKpTaTZTP5nkiKX/AJ6wkxt+YxmojFqlnzDMl9EP+Wc2Ek/BhwfxH40AaVFU7XVLe5l8g74LgDJgmG1/qOxHuMirlABRSZAoyKAFooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACikqo+qWaHa0w3ed5AUAkl8A4A78HNA0m9i5RTWZUUszBVUZJJwAKygJdcOTui03sOjXP+Cfqfp1BEjX89+7Q6Xt2KcPduMovqFH8Z/Qe/Sp7PTYLRjL80tww+eeU7nb8ew9hgVaREjRUjUIijCqowAPQU6gAooooAKKKKACs/Qf8AkC23+6f5mtCs/Qf+QLbf7p/maANCiiigAooooAgurK3vYvLuIhIoORngqfUHqD7iqJkvdJ/1pe9sx1kAzNEPcD749xz9a1aQ0AY/iAx6h4YufJbzY54wA0ZzuBYZxisuxF3P4h02W4SUfY1ltCSDhiF5b8flwfaovEGp3umq9z4TtWvZWkxcxxxF4Qf7wxj5s4Bx681rab9u1mwhuru+MG9R5lvajZ5bd1Zjlsg8HGKhq8jojJwpeTv+RsSzxQLumlSNfV2AH61TfXtKRtv26Jj6Id/8s06LRdNiIb7JHI4/jlHmN+bZNXVVVGFAA9AKs5zP/t7Tv+esn/fiT/4mhNf0p22/bolPpIdn88Vo0hUMMMAR6GgBkU8M67oZUkHqjA/yqSqMujabMSxs40f+/GNjfmuDUf2G+tubLUGkUf8ALK7G8f8AfQ+YfjmgDSorNXVxAwj1KBrNicCQndE30ft+OK0QcjI5FAC0UUUAFFFFABRRRQAUUUUAFFFFABRVO61O3tZBCS8twRkQQrucj1x2HucCoQdXuu0Ngh9f3sn9FH60AaVFZ39j+Z/x8397Me/77ywfwTFH9had3hc+5mc/1oA0K55dFu7bV5tVhIeZrk/unf5TCwUHH91sjPvjFaJ0O1X/AFMl1CfWO5cfoTiub8U2XiWea307QNWkckF7gSlVKIeBlwM4PPHXiplsbUW+blulfub5H9tzlf8AmHQtg/8ATw4P/oAP5n2HOr0rLi1EafGkF/afY40AVZY/mhwPcfdH1ArTVldQysGUjIIOQaoxHUUUUAFFFFABRRRQAVn6D/yBbb/dP8zWhWfoP/IFtv8AdP8AM0AaFFFFABRRVW+vUsogxVpJZDtiiX70jeg/qewoAdeXsFjEHmY5Y7URRlnb0UdzVMWVzqXz6kfLgP3bNG4P/XRh94+w4+tS2Vg6Sm8vWEt44xkfdiH91PQep6n9Kv0ANSNI0VI1CKowFUYAFZ15by2Vw2o2aFyf+PmBf+Wqj+If7Y/UceladFAEcE8VzAk0Lh45FDKw6EVJWWB/ZWoBRxZ3j8DtFKf6N/P61qUAFFFFABRRRQA1kV1KuoZWGCCMg1mmwuNOPmaWQ0X8Vm7fL/wA/wAJ9un061qUUAVrK+hvo2aLcrIdskbjDxn0I7VZqje2DSyLd2jiG8jGFcj5XH91x3H6jqKksb5byNsoYpojtmhbrG39R3B7igC1RRRQAUUUUAFFFFACEgDJ4ArL+03GrMVspDBZ5w10B80ntH7f7X5etEmdYneAEiwibbKR/wAt2HVR/sjv6njsa1FUKoVQAAMADtQBBaWVvYxmO3jCAnLHqzn1JPJPuasUUUAFFFFAEN1cx2drJcSnCRqWOOp9h71BpdtJDA01wB9quW8yb2PZfoowPwqK9/0vU7ay6xxf6RN74OEH/fWT/wABrSoAQgEEHkGs19OlsmM2lFUGcvascRv9P7h9xx6itOigCtZX0V9GxQMkiHbJE4w0behH9ehqzVG+spGkF5Z4S7jGBngSr/cb29D2P41NZ3cd7brMgK8kMjcMjDqp9waALFFFFABRRRQAVn6D/wAgW2/3T/M1oVn6D/yBbb/dP8zQBoUUUUAR3E8VtA88zhI41LMx7AVS0+3kmlOpXiFZpBiKM/8ALGP0/wB49T+Xam3A/tHVFtetvaESTf7T9UX8PvH/AIDWnQAUUUUAFFFFAEN3bR3lrJbyglJFwcdR7j3HWoNLuZJrdobg5ubdvKl9yOjfQjB/GrtZtz/oer290OI7n/R5f97kofzyv/AhQBpUUUUAFFFFABRRRQAVn6hbSpIuoWa5uYhhkH/LZO6n37g9j9TWhRQBFbXEV3bx3ELbo5F3KalrMiH9naqYRxbXpLx+iS9WH/Ahz9QfWtOgAooooAKoanPJtjsrdis90SoYdY1H3m/AdPcir9Zth/pV/d3zcqG+zw/7qn5j+LZ/75FAF6CCO2gSCFQkcahVA7CpKKKACiiigAooqrqdybTTLm4X70cTFfrjj9aAINJHnG6vjz9pmIQ/7C/Kv8ifxrRqCytxaWMFsvSKNU/IVPQAUUUUAFZlwP7O1FLteILlhHcDsrdEf/2U/h6Vp1DdW8d3ay28gykqlT+NAE1FU9KuJLiwQzEGeMmKX/fU4P54z+NXKACiiigArP0H/kC23+6f5mtCs/Qf+QLbf7p/maANCorq4S0tZbiT7kSFz+AqWs7Vv3zWllwRcTguPVF+Y/yA/GgCTSreS3sVMw/fzEyzf77ckfhwPwq7RRQAUUUUAFFFFABVXU7ZrzTpoUOJCuYz6OOVP5gVaooAgsrlbyyhuV6SoGx6ZHIqes/SAYlurUgAQXLhQP7rfOP/AEL9K0KACiiigAooooAKKKKAKep2rXdi6xYEyYkhPo68r+vH41LZ3K3lnDcpwJUDY9Pap6ztL/cXF7Z9opvMQf7L/N/6FuoA0aKKKAIbuf7NZz3HXyo2f8hmotKgNtpdtEfvCMbv948n9Sah14kaJcgfxKF/Mgf1rRoAKKKKACiiigArO1s5s4ov+e1zFGfpvBP6A1o1h+JdRtrL7Ak1zFBLJcZjMpwuQp5PoASv500m3ZAaVpqFvevOkLEmCTY+Rjn1HqOvPsatVzen/wBm6bdRSRa5byp5PlSrLcqehyCPxLfnWt/bWk/9BOz/AO/6/wCNVNRT93YC9RVH+2tJ/wCgnZ/9/wBf8aP7a0n/AKCdn/3/AF/xqAL1FUf7a0n/AKCdn/3/AF/xo/trSf8AoJ2f/f8AX/GgBlmPJ1i/h4CyBJ1HuQVP/oA/OtGsP+1dOPiKNk1C1ZWtGBImU9HXHf3NaX9qaf8A8/8Abf8Af5f8aALVFVf7U0//AJ/7b/v8v+NH9qaf/wA/9t/3+X/GgC1WHoWp2ywwaazFZ1tvP5GF27iOvrxWg+r6bHG0j6hbBVBLHzl4A/GuS077FqtjDe2mrWkeUSI73wwUM4kBB9VcY9wKAOv03UINVsY7y1LGGTO0suCcEjp+FQN+98RICOILUsPq7Y/khqhY3aaabWzS5sntmklaSRZQdgJZlHoBjAyalh1bTV1y9Z9QtV/dRKuZlGfvn196ANuiqP8AbWk/9BOz/wC/6/40f21pP/QTs/8Av+v+NAF6iqP9taT/ANBOz/7/AK/40f21pP8A0E7P/v8Ar/jQBeoqj/bWk/8AQTs/+/6/40f21pP/AEE7P/v+v+NAF6iqP9taT/0E7P8A7/r/AI0f21pP/QTs/wDv+v8AjQBXMy2Gq38sgYo8ULgKMknLJ/QVftrtLneFV0eM4dHGCOMisC8vrPU9baxtbyCV5rYAYfKllfdtyO+M8Vr6bZSWhmZgiLKwIjjJIXjk5Pc/0rTlSjd7gX6KKKzAKKKKACiiigArPP7rxCp6Ce1I+pRh/wDFmtCs6941vTW9RKv/AI6D/SgDRooooAzteBOiXRH8KhvyIP8AStGobqAXNpNbngSxsn5jFRaVObnS7aVvvGMB/wDeHB/UGgC3RRRQAUUUUAFY+u2FndzabJd28cxjuxt3jOMg/wBQPyrYrO1oYs45v+eNxFIfoHGf0JpptbAWP7Nsf+fK3/79L/hR/Ztj/wA+Vv8A9+l/wqzRSArf2bY/8+Vv/wB+l/wo/s2x/wCfK3/79L/hVmigCt/Ztj/z5W//AH6X/Cj+zbH/AJ8rf/v0v+FWaKAMc2Np/wAJHGq2kAVbRicRju647exrR+xWn/PrD/37FVbM+dq1/P1WPZAp+gLH9X/StGgCD7Faf8+sP/fsUfYrT/n1h/79ip6KAKz6fZSIyPZwMrDBBjHIrN8NaVp9toNtHDZQIuCcbAcnJ7mtus/Qf+QLbf7p/maALBsLMkH7LDkdPkFUILCzOuXqtaQHMUTDMY/2x6e1a9ZzfuvEMbE8T2pUfVGB/kxoAsf2bY/8+Vv/AN+l/wAKP7Nsf+fK3/79L/hVmigCt/Ztj/z5W/8A36X/AAo/s2x/58rf/v0v+FWaKAK39m2P/Plb/wDfpf8ACj+zbH/nyt/+/S/4VZooArf2bY/8+Vv/AN+l/wAKP7Nsf+fK3/79L/hVmigDFTS7OPxSLiO1iR0tM5VcYJbGcdM4BGa2qz7ZjJrt83aOKKMfX5mP8xWhTu2AUUUUgCiiigAooooAKzrznW9NX0Erf+Ogf1rRrPJ8zxCB1EFqfwLt/wDYUAaFFFFABWbYn7LqN1YnhXP2iH6MfmH4Nz/wIVpVQ1S3lZI7u2Xdc2rb0X++v8SfiP1AoAv0VFbXEV3bx3ELbo5Fyp/z3qWgAooooAKq6lbfa9NubcdZImUfXHH61aooAr2NyLywguR/y1jVvzFWKztKPkvd2J/5d5iyDH8D/MP1LD8K0aACiiigAqG7uY7O0luZPuRKWPv7VNWZOf7S1JbZeba0YSTHs0nVU/D7x/4DQBPpVs9tYRrNjznJkl/32OT+px+FXKKKACiiigArP0H/AJAtt/un+ZrQrP0H/kC23+6f5mgDQrO1f9z9lveALacbz/sN8p/mD+FaNRXMCXVtLbyDKSoUb6EUAS0VS0m4eeyCTHNxAxhm/wB5e/4jB/GrtABRRRQAUUUUAFFFVNTuWtNOmlj/ANZt2xj1c8KPzIoAi0gmWO5uiwYXFy7KR/dHyD9F/WtCoLO2Wzs4bZekSBc+uBU9ABRRRQAUUUUAFFFFABWdpf7+a9ve002xD/sp8v8AMMfxqXVLl7WxYxf6+QiOEertwPy6/QVNaWyWdpFbR/diQKCe+O9AE1FFFABRRRQBlTBtHuHukUtYytunQDJhbu4Hof4h+PrWmjrIgdGDKwyGByCKWsw2txpjmTT0822Jy9pnG31MZ6D/AHTx6YoA1KKrWl/b3qkwyZZeHjYbXQ+jKeRVmgAooooAzb7/AETUba/6Rv8A6PN7An5D+Dcf8CrSqK5t47u2kt5lzHKpVh7Gq2l3MkkL29wc3Nq3lyn+96N9COfzHagC9RSMyqpZiFAGSSelZrX8+oEx6WB5fRrxxlB/uD+M+/T69KAH317J5osbHBu3GSxGVhX+839B3PtmrNnaR2VssEWSByWY5LE8kk9yTzSWdlDYxFIsksdzu5yzt6k9zVigAooooAKKKKACs/Qf+QLbf7p/ma0Kz9B/5Att/un+ZoA0KKKKAMy6P9nakl70t7nEU/ordEf/ANlP4eladRzQx3ELwyoHjkUqynoQao2E8ltN/Zl25aRRmCVv+WyD/wBmHQ/n3oA0qKKKACiiigArNuP9N1iG2HMdoPPl/wB85CD+Z/AVbvLqOytZLiXO2MZwOrHsB7k8VDplrJb25e4wbmdjLMR2Y9h7AYH4UAXaKKKACiiigAooooAKKKztQuJJpRptm5WeQZkkH/LFPX6noB+PagBsB/tHVGuetvZkxxejydGb8Puj33Vp1HbwR2tvHBCgSONQqqOwqSgAooooAKKKKACiiigCpd6bbXjCR1KTKMJNG211+hH8ulQeXq9r/q5Yb6P0lHlyY/3gCD+QrSooAzhqsqf8fGmXkRHUqgkH/jpP8qP7dsh1Fyp9Dayf/E1o0UAZ39swt/qbW9l/3bZh+rACuc8UTeKhJb6hoOmmF0BSfzGRmdOoBXPQc9DnmuzrH0vULf7ff2st2nn/AGxgkTSDdjap4Hp1qZdjWldPmtexJbadHfxR3N7dG/VwGVekPqCEHX8c1qAAAADAHSsp86LO0yg/2fM26QD/AJd2PVh/snv6HnpmtUEEAg5B6GqMhaKKKACiiigAooooAKz9B/5Att/un+ZrQrP0H/kC23+6f5mgDQooooAKrX1lHfQCNiyOp3RyJw0bDoRVmigDPsr6TzvsV8FjuwMqRwswH8S/1HUfTmtCoLuzhvYfKnXIzlWBwyHsQex96pC6utL+W/DXFsOl0i/Mo/21H/oQ49QKANSimRSxzxrJFIsiMMqynIP41n3c0moTtp9q5SNeLqdT9wf3FP8AeP6D3xQAkf8AxNtQE3WztH/d+kso4LfReg98+grUpkUUcESQxIEjQBVVRwAKfQAUUUUAFFFFABRTJJEijaSR1RFGWZjgAe5rON5dan8mnAwwHrdyL1/3FPX6nj60AS3t+6yizslEt4wzg/diH95/b0HU/rUtjYpZQlQzSSu26WVvvSN6n/DsKdZ2UNlEY4VPzHc7scs7dyx7mrFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABTPKj37/AC13f3sDNPooAQqGBBAIPBBrL2SaKSUVpdP7ooy1v9B3T26j6dNWigBkUsc0ayROrowyrKcgin1nSWE1pI0+msqbjue2c4jkPqP7p9xx6jvUtrqUNzIYHDQXKj5oJRhvqOzD3FAFyiiigAooooAKz9B/5Att/un+ZrQrP0H/AJAtt/un+ZoA0KKKKACiiigAoqvd3tvZIGnk2ljhFAyzn0AHJqoYLvVP+PoNa2h/5YK37yQf7ZHQew/E9qAMHxDpF1rcbw+GbprBxJm4uI5GjikI/hG3q2eSR6YJrX05b/R7CC1mtBdrEgDTWx+Zz3ZlbuTycE03xBbSG10+2spTat9rQRtGMBcKxAIH8OQMil8O3c17JqUk8bxSLchHibPyMI1BA9s5IPvUfaN7N0vJFxNa08nbJcCBh1WdTGf/AB7FXI5Y5QGjkVwehVgaVkV1KuoZT1BGRVWTSdOk+9YwfhGBVmBcpjyxxDdJIqAd2OKo/wBg6XnP2NPzP+NSx6Rpsf3bGD8Ywf50AMfWtPU7UuBO3ZYAZD/47mm/atRueLayEC5/1l03P4IvP5kVfREjUKihVHYDAp1AGemko8izX0z3sqnK+YMIp9kHH4nJ960KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACoLmzt7yMR3ESyAHIz1U+oPUH6VPRQBneRqNn/wAe063cQ/5ZXBw4+jjr+I/GlGsQRkLeRy2THj98vy/g4yv61oUhGRg8g0ANjljmQPFIsinoynINPqjJo2nu/mC2WJ/78JMZ/NcU3+zJUOYdTvE9mZXH/jwJ/WgDQrP0H/kC23+6f5mg2mpA/Lqgx/tW6n+RFUNEtdSbR7YjUkVdp4FsPU+9AG/SEgDJOAKoHTrmT/W6rdY9IwifyXNL/YtizBpo3uGHeeRpP0JxQAsmsWSv5cUhuZP7lupkP444H40zdql591UsIj3bEkp/D7o/Wr0cccSBI0VFHRVGAKfQBVtdOt7VzKoaSZhhppDuc/j2HsOKtUUUAJijFLRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAf/2Q==)
6. Join AM and AN. Join BK and BL.
7. AM,AN,BK and BL are the required tangents.
![](data:image/jpeg;base64,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)
Question 6.⨀ (P, 4) is given. Draw a pair of tangents through A which is in the exterior of ⨀(P, 4) such that measure of an angle between the tangents is 60° .
Answer:Angle between the tangents =60°
We first find the angle between the radius.
Angle between radius + Angle between tangents =180°
⇒ Angle between radius = 180-60=120°
Steps of Construction:
1. Draw a circle of radius 4cm and center P.
2. Draw a radius on the circle. Draw another radius making 120° with this radius.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCADJAMUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKiuLmG0gae4lSKJBlnc4AoAlqOaeK3jMs0qRRjqzsAB+JrN+26hqXGnw/ZYD/y9XKHLe6x9fxbH0NSQ6HaLKJ7ove3AORLcndj/AHV6L+AoAZ/bsc/GnWlzff7cabY/++2wPyzS516c/dsrNT6lpmH/AKCK06WgDLGl38n+v1u5I9IYo4x/In9aX+xAfvanqLf9vJH8sVp0UAZn9hqPu6jqI/7emP8AOkOk3af6jW71T6SCOQfqtalFAGX5evQY2T2V2O/mRtEx/EEj9KT+2Jrf/kIabc26jrLGPOT815H4itWigCvaX1rfR+Za3Ecy9yjZx9fSrFUbvR7K8k85ojFcdp4WKSD/AIEP61XLatpv3h/aduO6gJOo+n3X/Q/WgDWoqtZaha6hEZLaUPtOHUjDIfRgeQfrVmgAooooAKKKKACiiigAooooAKKKzb+/l88afp4V7tl3MzDKQKf4m9/Qd/pQA+/1NbWRbW3iNzeSDKQIcYH95j/Cvv8Almo7bSWedbzU5BdXKnKLjEUP+4vr/tHn6VY0/TodPiYIWklkO6WaQ5eRvUn+nQVboAKKKKACiiigAooooAKKKKACiiigAooooAoX2lRXUouYna2u1GFuIvvfRh0YexqO11KWK4Sx1RFhuH4ilX/VT/7p7N/sn8M1p1Dd2kF7btb3MYkjfqD/ADHofegCaismC5n0u4Sy1CQywyHbbXbdSeyP/teh7/XrrUAFFFFABRRRQAUUVBeXcVjaS3U7bY4l3HHX6D37UAV9TvpIPLtbRVkvbjIiU9FA6u3+yP1OB3qTT7CPT7corGSRzvllb70jHqx/zx0qHSrSVfMvrxcXlzguOvlL/DGPp39STWjQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAEVzbQ3du9vcRiSKQYZT3rPsLiazuhpd65dtpNtO3WZB1B/wBsd/Uc+tatVNSsVv7Ux7jHKpDwyjrG46MP88jIoAt0VR0vUPtsBWYLHdwkpPFn7rDuPY8EH0NXqACiiigArJmH9p60tv1trAiST0eU8qP+Aj5vqVq9fXaWNjNdScrEhbHqew/E8VDpFo9np6LNzcSEyzn1kblv8PoBQBeooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiqd7qdtZMsbFpJ3+5BENzt+HYe54oAuVmz6uGma10+E3twpwwU4jjP+2/QfQZPtUf2O/1PnUJDa25/wCXWB/mb/fcfyXH1NaUFvDbQrDBEkUaDCqgwBQBy02jXGm69B4gvLtJd8oW4Ece3ywy7BznlAcdfrXWVHc28d1bSW8y7o5UKMPUGqeizySWRguG3XFq5glP94r0b8VwfxqpSctwNGiiipAy9U/0q/sLDqrSGeUf7KYI/wDHiv5VqVl2eLjX7+4xxAkdup/De3/oS/lWpQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUjMFUsxAAGST2oAWobq7t7KEzXMyxRjux/Qepqg2qTXxMekxCUdDdSZES/Tu5+nHvUtrpMcUwurmRru7HSaX+D/AHV6KPpz70AQ+dqOqcW6tp9qf+Wsi/vnH+yp4X6nn2q5ZadbWCt5Efzvy8jnc7n1ZjyatUUAFFFFABWWf9D8SA9Ev4cf9tI/8VP/AI7WpWXrv7q2t7wdbW5jkJ/2SdrfoxoA1KKKKAMzQsPa3Fx/z3upX/AMVH6KK06zPDgxoFof7yFvzJP9a06ACiiigAooooAKKKKACiiigBKKyvEcjx2EWxphuuYlYQHDsC3IFN0ZLlbm4JW7SzKr5a3bbn3c7iOSQOnWtFD3Oa4jYpKpahrFlpsaNcTZeTiKKMb5JT6Ko5NZ1vPf6zcy292r6bCqhxCjgyyKc/eYfd5HIHPvWVwuX7nVo45ja2sbXd0OsUR4T/ebov48+1RrpU16wk1aUTAHK20eRCv17ufrx7VetrW3s4RDbQrFGP4VH6+5qamMQKFAVQAAMADtS0UUAFFFFABRRRQAVT1eH7Ro95FjJeBwPrg4q5TWUMpU9CMUAQ2M/wBpsLec8mWJX/MA0VW8Ptu0Cx9oVX8hiigBPDpz4fsv+uQFaVZnh35dGjjPWKSSM/g7CtOgAooooAKKKKACiiigAooooAhntorkIJV3BHWReejA5BqLVLL+0dMubITPB58ZTzE6rkdat0lO7QHG+CNKhsNChusK9xdDe0m3lR2UH04/Wty0+fW5pAflgtxG5/2id2Py/nWZ4cj1J/D1jDFAkAEWPOlYN3PIUdfxxVjxBpkcPhS8iWaYBInlch8GVsdWP17f0qZylJuT3M/M32lRNoZ1UscKCcZPtR5ibwm5Q5GQuecVzHiFdOnuPseIX1C4twoedwFtY8n95z0OemOSQOwqpIIVnnZmV9UXVYlhYn94Y/kxjvtKbie3Wpcgc7M7NXVs7WBwcHB6GnVR0/S4tOaZonZvNOfmA4HPp16nk81eq0WgooooGFFFFABRRUN1KILSaY9I42Y/gM0AU/D3/IAs/ePP60VJosZi0SxQ9Rbpn/vkUUAQ6QfLutStT1jui6/7rqG/nurUrLc/ZvEsbZwl7blP+Bocj/x1m/KtSgAooooAKKKKACiiigAooooAKKKKAMzw5/yL1j/1yFaLosiFHUMrDBBGQazvDn/IvWP/AFyFadAFabTbG5ffcWdvK+MbpIlY4/EU/wCywecs3kx+aq7VfYNwHoD6VNRRYVkJS0UUDCiiigAooooAKzfEDldEuUX70yiFfq5C/wBa0qy9S/0jVNOswMgSG4k9gg4/8eZfyoA0kRY0VFGFUYAop1FAGbrkTmwF1Cu6azcXCD12/eH4qWH41filSeFJY2DJIoZSO4PSnGsvST9jnn0l+kB8yDPeJjwP+AnK/lQBq0UUUAFFFFABRRRQAUUUUAFJkHNUtZvZ9P0qe6trWS7nRf3cMalixJwOBzgZyfYVg+BZQf7Zh/0xnW/LvJdRMhdmjTPB6c547AigDZ8Of8i9Y/8AXIVp1meHP+Resf8ArkK06ACiiigAooooAKKKKACiiigArL0z/S9RvdRPK7vs8J/2UJ3H8WJ/IVLq91Jb2fl2/wDx83DCGD2Y9/oBk/hViztY7KzitYRhIkCj396AJ6KKKACs7VreXEV/aoWubQlgo6yIfvJ+I5HuBWjRQBFbXMV3bR3EDh45FDKw7ipayCf7Fvi3TT7uTn0glP8AJWP5H61r0AFFFFABRRRQAUUUUAFMSKOMuyIql23OQMbjjGT6ngU+igDM8Of8i9Y/9chWnWZ4c/5F6x/65CtOgAooooAKKKKACiiigApCcUtZN/I2pXJ0q3YiMAG8lU/dU/wD/ab9B9RQAWH/ABMr99UbmCMGK0B7j+J/xIwPYe9a1NjRYkWNFCooAVQMAAdqdQAUUUUAFFFFADJoY54nhlQPG4KsrDIIPasu3nk0idLG8dmtnO21uWP5RufX0Pf69deori3huoHgnjWSKQYZWHBFAEtFYyz3Ghny7tnn0/olyeXh9pPUf7X5+ta6OsiB0YMrDIIOQRQA6iiigAooooAKKKKAMzw5/wAi9Y/9chWnWZ4c/wCResf+uQrToAKKKKACiiigAoorKn1Ca9maz0kqWU7ZrojKQ+w/vN7dB39KAH39/Kbgafp+Gu2GXcjK26n+Jvf0Hf6VasbKKwtlhiyeSzOxyzserE9yaSxsIdPgMcO4ljueRzlpGPVmPc1ZoAKKKKACiiigAooooAKKKKAEIBGDyKym024092l0hlCE7ns5DiNv90/wH9PataigChaavb3M32aQPa3fe3mG1j7jsw9xmr9QXdla30Pk3UCSp1AYdD6g9j9Ko/YNSsv+PC+86If8sLzLY9g45H45oA1aKyv7aa341HT7m19XVfNj/wC+l6fiBVu11Kxvf+Pa7hmPojgn8qALVFFJQBm+HP8AkXrH/rkK06zPDn/IvWP/AFyFadABRUNxd21ou64uIoV9ZHC/zqidegmythb3F83Ywx4T/vtsL+tAGpVS91O1sNomkzI/3IkG6R/oo5NVfJ1i+/188enxHqkH7yX8XIwPwB+tWrLTLSw3NBF+8f78rks7/VjyaAKZt7/Vv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3. From the points on the circumference on the circle, draw perpendiculars to these radius.
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCACwAOsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAoopCQBk8CgBaiuLmC1haa4mSGNeruwUD8TWa2qXGouYtGjR0Bw15Lnyl/3R1c/Tj3qW30S3SZbm7d766HIluOdv+6vRfwFAEf9tvc/8gzT7i7HaVh5Uf8A303J/AGlEWvXH+surOzHpFEZW/NiB+latFAGWdHuJOZtav2P/TMpGP0Wk/sIf9BTU/8AwJP+FatFAGWNIuI+YdavlP8A00KSD9VpDFr1v/q7qzvB6SxGJvzUkfpWrRQBlf221t/yE9PuLQd5QPNj/wC+l5H4gVoQXEF1Cs1vMk0bdHRgwP4ipazbjRLd5mubN3sbo8mWDA3f7y9G/EUAaVFZC6pcae6w6zGkak4S8iz5Tf73dD9ePetYHIyORQAtFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRSEgAknAHU0AMmmit4XmmkWOOMFmdjgAVkLDP4g/eXSvBpvWO3PyvcD+8/ovovfv6UsK/2/cLdSj/iWwtm3jP/AC8MP+Wjf7I/hHfr6VtUANRFjQIihVUYCgYAFOoooAKKKKACiiigAooooAKKKKAGuiyIyOoZWGCpGQRWM0M/h/8AeWyvPpnV7cfM9uP7yeq+q9u3pW3RQBHDNHcQpNDIskbgMrKcgj1FSVizL/wj9y1zGP8AiWzNmeMf8u7H/loP9kn7w7dfWthnUIXLDaBkn2oAdRWPpGpyXdw8c0iN5qedCFIyqZxtPuOD+NbFVKLi7MAoooqQCiiigAooooAKKKKACiiigArI1Nm1K7XR42IjK+ZeMD0j7J9WIP4A+orRu7mKytJbqY4jhQux9hVTRbWSCzM9yMXd23nT+xPRfoowPwoAvqqooVVCqowABgAU6iigAooooAKKKKACiiigAooooAKKKKACiioLu9trCHzrqZYkzgFupPoB1J9hQBK6q6MjqGVhggjIIrl1v7eyu5fC88kxjYqkEyc7EfpG3fjoD6EVY1O71e6szNbrJp1krAyyFQbho+5VeiY685OOwrO1bQrKx037fpqJFf2ji4hnkkJadxztdifm3DI/EY6U4yinqS2dO2nW/nwTRIIXgJxsUDcCMEH2/wAKuVT0rUoNX0u21C2J8q4jDgHqvqD7g8H6Vcobb3KCiiikAUUUUAFFFFABRRRQAUUUUAZWr/6Vd2Om9Vmk86UeqR4OPxYoPzrVrLtB5/iK+nPS3ijt1+py7fzX8q1KACiiigAooooAKKKKACiiigAooooAKa7rGhd2CqoyWJwAKoXOros7WtlE17dLw0cZwsf++3Rfp19qjTSJLtxNq8wuSDlbdBiFPw/iPu35CgBDqlxqBKaREHTobyYERD/dHV/wwPeprTSYbeb7VO73d3j/AF83JX2UdFH0q+AAAAMAdKyfEsTzaLKiyKo3xl1eTYJF3jKbu24cfjSbshN2VzUJRkJJUoRznpiqFpo9naOkmWmZeITK27yx2Cjt/OuXjCyaobKS1W10x9QiVrUsCqt5LHacccsFJUcZx61paXpceoQyqszJb2l9KluFwQE3KcKT0wwIBHQZFQpXexmpcz2E0gnQ/EV9ph4s7qfzoPSN3BOPoxD/AIr711NYWs2SXGq20bsUW7heDevVXXEiMPcEMRV/Sb17y0InULdQMYrhB2cdx7EYI9jWhqXqKKKACiiigAooooAKKKKACiiigDL0P51v5v8Anrey/wDjpCf+y1qVl+H/APkGv6/aZ8/9/WrUoAKKKKACiiigApKWkoA5yDX70wW11KbJ455xF5EZIlGW28c8kdTx610lZulaPb6daxq0MDXCbszLGAxySevXvXPahqniWXxi+jWxS1s2jD+cIgzLHjlwScbt3y4I/Ct5qM2+TS1xbHSalrVjpRjS5mAmlOIoUG6SQ+y/16VB9m1DVOb1zZWx/wCXaF/3jj/bcdPov51nz6VZ6fpN68as0zxFpLiVt8shAyCWPPXHHT2ro4ixiQt94qM/WudPUSd2NtrWCzgWC2hSKNeioMCpaSimULUc0Mc8TRTRrJG4wyOMgj3FSUUAVBpdgLI2Qs4BbHrF5Y2n8KnggitoVhgjWKNBhUQYAHsKkoosKyMvWxt/s+Yf8s72P/x7Kf8As1M1D/iWajHqq8QS4hux6DPySfgTg+x9qk8Qf8g6P1+1QY/7+rWhNFHPC8MqB45FKsp6EHqKBj6Ky9Hmkh83Srly01ngI7dZIj9xvrxg+4961KACiiigAooooAKKKKACiiigDL0L5YbyH/nlezD823D9GFalZdj+413Urc8CXy7hfxXYf1T9a1KACiiigAooooAKKKKACueu5Y4vGRaSRUX+zOrMAP8AW10NY0ttBP4sBmhjkK2I2l1Bx+87UmJjF/4m8ixxAmyVg0spGBLg5Cr6jPU9O1Ntb/WLm41e38q3jngEf2aNmyF3KT8xHX14+lbuMDFZlzo7SnUngvJbeW/RF8xAMxbRjK++DU2ZPK1sZJ1bUoZp7FL2O6JuIbdLvyQBHI5O9cDhioAP1ODU63etSC5s4JEnuLO48t5QiqXUoGQkHgcnBx6cVND4ckj04WT6gSkTI9sY4EQwupyG46++evPrV/TdO+wRyl5muJ55PMmlcAFmwB0HQAAACkkyUpdS4ucDPXHOKdRRWhqFFFFAGXrhzHZRdfNvYh+Tbv8A2WtSsu+/f69ptv1EQkuG/AbB/wChn8q1KAMvWIZIvK1S2QtPZ5LIvWWI/fX68ZHuBWhDNHcQpNE4eORQysOhB6GpKyNP/wCJXqMmltxBLumtD2Az88f4E5HsfagDXooooAKKKKACiiigAooooAytR/0XVtPvuiMxtZT7Pgqf++lA/wCBVq1W1GzXUNPmtWO3zFwGH8J6g/gcH8Kj0m9a+sEklXbOhMc6f3ZF4YfnyPYigC7RRRQAUUUUAFFFFADGkjQqruqlztUE43HrgflWcP8Akaz/ANeI/wDQzXL6td3UvjHTLi70u/UQaj5FpiMGPYYn3PndyWPPThV+tdQP+RrP/XiP/QzQBqUUUUAFFFFABRRRQAUUVS1e9axsHeIbriQiOBP70jcL/ifYGgCvpv8ApWq6hf8AVAwtoj7Jncf++mI/4DWrVbT7NdPsIbRDuES4LHqx7n8Tk/jVmgAqjq1k95aAwMEuoGEtu57OOmfY8g+xNXqKAKunX0eo2SXMY25yHQ9Y2HDKfcHIq1WOQNJ1oOAFtNRfDY6JPjg/8CAx9QPWtigAooooAKKKKACiiigArHuj/ZOqi+6Wl2VjufSN+iP9D90/8BrYqOaGO4heGZA8cilXVhwQeooAkorIsJ5NOuV0m8csCD9knY/61R/AT/fUfmOfWtegAooooAKKKKAGtGjlSyKxQ5UkZwfUVmj/AJGs/wDXiP8A0M1qVlj/AJGs/wDXiP8A0M0AalFJRmgBaKTNLQAUUUUAFY9of7W1Q3/W0tC0dt6SP0eT6D7o/wCBetLfzyaldNpNm5VR/wAfk6n/AFan+BT/AHyPyHPpWpDDHbwpDCgSONQqqvQAdBQA+iiigAooooAr31nHf2UtrLkJIuMjqp7Ee4OD+FV9IvJLm2aG6wLu2bypwO7Dow9mGCPrWhWRqY/s69j1hOIgBFdgf8888P8A8BJ/ImgDXopAc0tABRRRQAUUUUAFFFFAFe9soL+2aCdSVJBBBwykdCD2I9apW19NYzJY6owJY7YLrGFm9A391/boe3pWrUc9vDdQPBPGskbjDIwyCKAJKKyRFf6T/wAe++/sx/yyZv30Q/2WP3x7Hn3NXLPUbW/Vvs8oZk+/Gw2uh91PIoAtUUUUAFZf/M1n/rxH/oZrUrDur+1svFQ+0TCPdY8cE5/ee1AD/EL3Cx2m1rlLQz/6W1sCZAm04xjnG7Gcc4rH0y5utXvV02a7vIoITcFXDlJXCuqpuPXgMfrxmtySTS9dxbrcMZIj5qmJmjdD0yDx64/Glk8Pae9tDAqyxCDdskilZX+b72WByd3fPWs2m3dGTi27opaL/aOpW2najJd/KYh5i5I3EbgTgcHdweemOK6AVHb28VrBHBAgjijUKiKOFA6CorzUbWwC/aJQHf7kags7/RRyatKyLirItVlXF9PfzPY6WwBU7Z7vGVh9Qv8Aef8AQd/SmmG/1b/j432Fmf8AlirfvpR/tMPuD2HPuK04IIraFIYI1jjQYVFGABTKI7KygsLZbe3XCjkknJYnqSe5PrViiigAooooAKKKKACmyIksbRyKGRwVZSOCD1FOooAytHka1kl0idiXtQDAzdZIT90/UfdP0B71q1maxby7ItQtVLXNmS6qOsiH76fiOnuBVl76JtLbUIT5sXkmVcfxDGaBpXdizmlrn9PttSntLLVG1h/NmCSSwsq+SVbnaoxkHng561vjpSTuVOPK7XuLRRRTICiiigAooooAKp3ulWd+VeaLEqfcmRikifRhzVyigDJFrrNn/wAe17FexjpHdrtcf8DXr+K0v9sXMPF5o93H/tQgTL/46c/pWrRQBlf8JJpQ/wBZcNCfSaF0/mKwLjxLpKeLDdNdqtr9k+z/AGg/c8zfu25+n68V1eoXRsrGa5VQ5jXIUnGazbSK1m1xpprG1+2eXuE8L7+OnPAwff0rSMLxbYmZP/CY+H4tZjmOqRyItsykxqz8llOOB7Vc/wCE3sJv+PONn9GnkWFf/Hjn9K6MKo/hH5Uu1f7o/KskrAlY5k6uLzi68QWNnGesdowZiP8Afb+i1asr7w1YFngvrbzX+/K8u+R/qx5rc2r/AHR+VG1f7o/KmMzv+Ei0b/oJ23/fwUf8JFo3/QTtv+/grR2r/dH5UbV/uj8qAM7/AISLRv8AoJ23/fwUf8JFo3/QTtv+/grR2r/dH5UbV/uj8qAM1vEmiIMtqlqBnHMgpf8AhItG/wCgnbf9/BWhsX+6Pypdq/3R+VAGd/wkWjf9BO2/7+Cj/hItG/6Cdt/38FaO1f7o/Kjav90flQBnf8JFo3/QTtv+/go/4SLRv+gnbf8AfwVo7V/uj8qNq/3R+VAGd/wkWjf9BO2/7+CuYk8b6L4f1l9LMpuLO4YSrJDhkty5O5T7Z+bjpk12+1f7o/KsXXfC2nay63j20f8AaEABgnOflKnK5HQjPr6mple2hrSdNS/eJ28ijFH4aieJf7Z3W0LiSK0e5BiRgcjA64B6AnArYHiLRv8AoJ23/fwVNpt4moWST+X5cnKyxnrG44ZT9DVvav8AdH5U0kiJTlL4mZ3/AAkWjf8AQTtv+/go/wCEi0b/AKCdt/38FaO1f7o/Kjav90flTJFooooAKKKKACiiigAooooAqanbPeadPbx7Q8i4G7p+NVrTT5k1Bbloba2VYyhSDPz5I68Dpj9a1KKtTajyisFFFFQMKKKKACiiigAooooAKKKKACiiigAooooAKKKKAMib/iVaytz0tb9hHN6JL0Vv+BD5T7ha16gvLSK+tJbWdcxyrtbHUe49+9VdHu5ZoJLW6bN3aN5cx/v/AN1x7MOfrkdqANGiiigD/9k=)
4. They intersect each other at one point.
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Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct two tangents to the circle from this point. Measure them.
Answer:
Steps of Construction:
1. Draw a circle of radius 5cm and center O.
2. Draw a line OP such that OP= 8cm
3. Draw a perpendicular bisector of OP which cuts OP at M.
4. Taking M as center and radius OM, draw a circle.
5. The two circles intersect at A and B.
6. Join AP and BP. AB and BP are the required tangents.
Question 2.
Draw ⨀ (O, 4). Construct a pair of tangents from A where OA = 10 units.
Answer:
Steps of Construction:
1. Draw a circle of radius 4cm and center O.
2. Draw a line OA such that OA= 10cm
3. Draw a perpendicular bisector of OA which cuts OA at M.
4. Taking M as center and radius OM, draw a circle.
5. The two circles intersect at P and Q.
6. Join AP and AQ. AP and AQ are the required tangents.
Question 3.
Draw a circle with the help of a circular bangle. Construct two tangents to this circle through a point in the exterior of the circle.
Answer:
Steps of construction:
1. Draw a circle(Say C1) with the help of a bangle, and take any three points A, B and C on its circumference
2. Join AB and BC and draw the perpendicular bisector of AB and BC which intersect each other at O.
3. O is the center of circle, now take any point P outside the circle and join OP.
4. Draw the perpendicular bisector of OP, which intersect OP at O'.
5. Taking O' as center and O'O = O'P as radius, draw a circle C2, which intersects the previous circle at Q and R.
6. Join PQ and PR, which are required tangents.
Question 4.
Draw ⨀(O, r). is a diameter of 0(0, r) . Points A and B are on the
such that A—P—Q and P—Q—B. Construct tangents through A and B to ⨀(O, r) .
Answer:
Steps of Construction:
1. Draw a circle of any radius(r ) and center O. Draw a diameter PQ of this circle.
2. Extend PQ both the sides as APQB is a straight line.
3. Draw a perpendicular bisector of OA and OB which cuts OA and OB.
4. Taking OA and OB as diameters, draw two circles.
5. The three circles intersect at K,L and M,N.
6. Join AK and AL. Join BM and BN.
7. AK,AL,BM and BN are the required tangents.
Question 5.
Draw AB such that AB = 10 cm. Draw ⨀(A, 3) and ⨀(B, 4). Construct tangents to each circle through the centre of the other circle.
Answer:
Steps of Construction:
1. Draw a circle of any radius 3 and center A.
2. With A as center, draw a circle of radius 3 cm. With B as center, draw a circle of radius 4cm.
3. Draw a perpendicular bisector of AB which cuts AB at M.
4. With M as center and AM as radius, draw a circle.
5. The three circles intersect at K,L and M,N.
6. Join AM and AN. Join BK and BL.
7. AM,AN,BK and BL are the required tangents.
Question 6.
⨀ (P, 4) is given. Draw a pair of tangents through A which is in the exterior of ⨀(P, 4) such that measure of an angle between the tangents is 60° .
Answer:
Angle between the tangents =60°
We first find the angle between the radius.
Angle between radius + Angle between tangents =180°
⇒ Angle between radius = 180-60=120°
Steps of Construction:
1. Draw a circle of radius 4cm and center P.
2. Draw a radius on the circle. Draw another radius making 120° with this radius.
3. From the points on the circumference on the circle, draw perpendiculars to these radius.
4. They intersect each other at one point.