In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ADC.
45∘
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 it at any point on the remaining part of the circle.
So,∠ADC=12∠AOC=12×90∘=45∘
∴∠ADC=45∘