Question

In the given figure, PA and PB are tangents to a circle centred at O. Prove that

1. OP bisects ∠APB
2. OP is the right bisector of AB.

Answer 1

i. ΔOAP ≅ ΔOBP

∠APO = ∠BPO

Or OP bisects ∠P

ii. ΔAQP ≅ ΔBQP

⇒ AQ = QB and ∠AQP = ∠BQP

AB is a straight line.

Therefore, ∠AQP = ∠BQP = 90°

Hence, OP is the right bisector of AB.