Question

In Fig. 9.23, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

Answer 1

It can be observed that 

∠AOC = ∠AOB + ∠BOC 

= 60° + 30° 

= 90° 

We know that angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.

∠ADC=\(\frac{1}{2}\)∠AOC=\(\frac{1}{2}\)× 90°= 45°