Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Step1: Taking O as a center, Draw a circle of 5cm Radius.

Step2: Now take point P at circumference and join OP. Draw a perpendicular to OP at point P.

Step3: Draw a radius OQ and an angle of with OA.

Step4: Now again draw a perpendicular to OQ at point Q.

Both perpendiculars intersect at point A. AP and AQ are tangents at angle .

Justification:

∠PAQ=60°

By construction,

∠OPA=90°

∠OQA=90°

And ∠POQ=120°

We know, the sum of all interior angles of a quadrilateral is

∠PAQ+∠OPA+∠OQA+∠POQ=360°

∠PAQ+ 90° +90° +120° =360°

∠PAQ=60°

Hence proved.