Question

In the given figure, PA and PB are tangents to a circle centred at O. Prove that (i) OP bisects ∠APB (ii) OP is the right bisector of AB. 

Answer 1

(i) △OAP ⩭ △OBP

∠APO= ∠BPO

Or OP bisects ∠P

(ii)△AQP ⩭ △BQP

⇒AQ=QB and ∠AQP = ∠BQP

AB is a straight line

Therefore ∠AQP = ∠BQP = 90°

Hence OP is the right bisector of AB