KöMaL 2013 B4534

$M$ and $N$ are points on the longest side, $AB$ of a triangle ABC , such that $BM$=$BC$ and $AN$=$AC$. The parallel drawn through point $M$ to the side $BC$intersects side $AC$ at $P$, and the parallel drawn through point $N$ to the side $AC$ intersects side $BC$ at $Q$. Prove that $CP$=$CQ$.