### Constructions Class 10th Mathematics Gujarat Board Solution

##### 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 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. PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

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# 2019 Board Paper Solution

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