Problem

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013

Tags: geometry, incircle, angle bisector



Let $M$ and $N$ be touching points of incircle with sides $AB$ and $AC$ of triangle $ABC$, and $P$ intersection point of line $MN$ and angle bisector of $\angle ABC$. Prove that $\angle BPC =90 ^{\circ}$