Question 17
Points $M$, $N$ and $P$ are chosen on the sides $BC$, $CA$ and $AB$ of triangle $ABC$ so that $BM = BP$ and $CM = CN$. The lowered perpendicular from $B$ to $MP$ and the lowered perpendicular of $C$ to $MN$ intersect $I$. Prove that the angles $\angle IPA$ and $\angle INC$ are congruent. 