Question

Draw a circle of radius 3cm,draw a pair of tangents to this circle inclined to each other answer by sarthaks

Answer 1

Steps of Construction:

Step I: Draw a circle with centre O and radius 3 cm.

Step II: Draw any diameter AOB.

Step III: Draw a radius OC such that ∠ BOC = 60°.

Step IV: At C, we draw CM ⊥ OC and at A, we draw AN ⊥ OA.

Step V: Let the two perpendiculars intersect each other at P.

Then, PA and PC are required tangents.

Justification:

Since OA is the radius, so PA has to be a tangent to the circle. Similarly, PC is also tangent to the circle.

∠APC = 360° – (∠OAP + ∠OCP + ∠AOC)

= 360° – (90° + 90° + 120°) = 360° – 300° = 60°

Hence, tangents PA and PC are inclined to each other at an angle of 60°.

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