assume point O is the center of the circumcircle of triangle ABC, and the bisector of angle A is extended to?

Question

meet the circle at P. prove that radius OP is perpendicular to BC

Answer 1

since this is a triangle inside of a circle. The bisector would mean an even cut of both the triangle and the circle. Because that's the only way that point O would be at the center of both the triangle and circle. So the triangle has to be at least an isosceles triangle. Then that means an even cut (OP) would make it perpendicular to the the base which is BC.