Problem

Source: 2012 Indonesia Round 2.5 TST 1 Problem 3

Tags: geometry, geometry proposed, Angle Chasing, complex numbers, cyclic quadrilateral



The incircle of a triangle $ABC$ is tangent to the sides $AB,AC$ at $M,N$ respectively. Suppose $P$ is the intersection between $MN$ and the bisector of $\angle ABC$. Prove that $BP$ and $CP$ are perpendicular.