Question

In Fig., 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

∠AOB + ∠BOC = 60° + 30° = 90° 

∴ ∠AOC = 90° 

(Angle subtended at the centre) 

∠ADC = ? 

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

∴ Angle subtended at the centre 

∠AOC= 2 × ∠ADC 

90° = 2 × ∠ADC 90 

∴ ∠ADC = \(\frac{90}{2}\)= 45° 

∴ ∠ADC = 45°.