Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°. (CBSE 2011)

1. Draw a circle with a radius of 3 cm and mark the center as O. Mark a point A on the circumference and join A to O.

2. Make an angle OAP of 90° with OA at A. This will be the tangent at A.

3. Draw a line OB at the center O such that B lies on the circle which makes 120° with AO, thus AOB is 120°. (∵ Tangents will make an angle of 90° each with the lines OA and OB and the angle between the tangents is 60°, therefore ∠AOB must have to be 120° as the sum of all angles of a quadrilateral is 360°).

4. At point B make an angle of 90° with BO. This will be the tangent at B.

5. Now, where these two tangents will intersect, that will be the point P which makes an angle of 60° between both the tangents.

∴ PA and PB are the required tangents.