Question

In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If angle ACO = 30°, find: angle APB

Answer 1

In the given fig, O is the centre of the circle and CA and CB are the tangents to the circle from C. Also,  ∠ ACO = 30°

P is any point on the circle. P and PB are joined.

To find : ∠ APB

Proof : 

Arc AB subtends ∠ AOB at the centre and  ∠ APB

is in the remaining part of the circle.

∴  `∠ "APB" = 1/2  ∠ "AOB"  =1/2 xx120 = 60°`