Question

In the given figure ABC is an isosceles triangle and O is the centre of its circumcircle. Prove that AP bisects angle BPC .

Answer 1

Given –
∆ABC is an isosceles triangle and O is the centre of its circumcircle
To prove –
AP bisects ∠BPC
Proof –
Chord AB subtends ∠APB and chord AC subtends ∠APC at the Circumference of the circle.
But chord AB = Chord AC
∴ ∠APB = ∠APC
∴ AP is the bisector of ∠BPC