Question

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find :  ∠ACB 

Answer 1

In cyclic quadrilateral AOBC,

∠ACB =180° - ∠AOB = 180° -150° = 30° 

(pair of opposite angles in a cyclic quadrilateral are supplementary)