Question

In the 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

We have, ∠BOC = 30° and ∠AOB = 60° 

∠AOC = ∠AOB + ∠BOC = 60° + 30° = 90° 

We know that angle subtended by an arc at the centre of a circle is double the angle subtended by the same arc on the remaining part of the circle. 

∴ 2∠ADC = ∠AOC 

⇒ ∠ADC = 1/ 2 ∠AOC = 1/ 2 × 90° 

⇒ ∠ADC = 45° Ans