From a point P outside the circle, with centre O, tangents PA and PB are drawn. Prove that: i) ∠AOP = ∠BOP ii) OP is the ⊥ bisector of chord AB.

According to the given question,

1. i) In 

      

   , we have

   

   

   

   

By SAS criterion of congruence

   

By C.P.C.T we have

   

1. ii) In

      

   , we have

   

   

   

By SAS criterion of congruence

   

By C.P.C.T we have

   

And

   

Since,

   

So,

   

Therefore,

   

is the perpendicular bisector of

   

– Hence Proved