MathNet 2014 Question 27

The points $M$, $N$, and $P$ are chosen on the sides $BC$, $CA$ and $AB$ of the triangle $ABC$ such that $BM = BP$ and $CM = CN$. The perpendicular dropped from $B$ onto $MP$ and the perpendicular dropped from $C$ onto $MN$ intersect at $I$. Prove that the angles $\widehat{IPA}$ and $\widehat{INC}$ are congruent.

Gabriel Popa