Classic geometry and sometimes a lemma - BIH JBMO TST 2013 - Problem 3

LaTeX: 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 $\angle BPC =90 ^{\circ}$