Question

ABC is an isosceles triangle in which BA = BC. Prove that the line segment joining the centre O of the circumcircle of triangle ABC to the vertex B bisects Angle ABC.​

Answer 1

As tangents drawn from an external point to a circle are equal in length.

So, therefore, we get AP=AQ (tangents from A)

BP=BR (tangent from B)

CQ=CR (tangent from C)

It is given that ABC is an isosceler triangle with sides AB=AC

⇒AB−AP=AC−AP

⇒AB−AP=AC−AQ

⇒BR=CQ

⇒BR=CR

So, therefore, BR=CR that imples BC is bisected at the point of contact.