Question

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

Answer 1

Steps of construction:

1. Draw a circle with a radius of 5 cm with the centre as O.
2. Take point A on the circumference of the circle and join OA. 
3. Draw a radius OB, making an angle of 120° (180° – 60°) with OA.
4. Draw a perpendicular to OB at point B and a perpendicular to OA at point A. Let both perpendiculars intersect at point P.
5. PA and PB are the required tangents at an angle of 60°.