Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60°. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Steps of construction:

1. Construct a circle with O as centre and a 4 cm radius

2. Construct any diameter AOB

3. Construct an angle ∠AOP = 60º where OP is the radius that intersects the circle at the point P

4. Construct PQ perpendicular to OP and BE perpendicular to OB

PQ and BE intersect at the point R

5. RP and RB are the required tangents

6. The measurement of OR is 8 cm

Explanation:

PR is the tangent to a circle

∠OPQ = 90º

BR is the tangent to a circle

∠OBR = 90º

So we get

∠POB = 180 - 60 = 120º

In BOPR

∠BRP = 360 - (120 + 90 + 90) = 60º

Therefore, the distance between the centre of the circle and the point of intersection of tangents is 8 cm.