Question

In the given figure, 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 the angle subtended by an arc at the centre is double the angle subtended by any point on the remaining part of the circle.

∠ADC = `1/2angleAOC`

= `1/2 xx 90^@`

= 45°