Question 173
Points $N$, $K$, $L$ lie on the sides $AB$, $BC$, $CA$ of a triangle $ABC$ respectively so that $AL = BK$ and $CN$ is the bisector of the angle $C$. The segments $AK$ and $BL$ meet at the point $P$. Let $I$ and $J$ be the incentres of the triangles $APL$ and $BPK$ respectively. The lines $CN$ and $IJ$ meet at point $Q$. Prove that $IP = JQ$.