AT-OEMO-FED1 2014 Problem 4

We are given a right-angled triangle $MNP$ with right angle in $P$ . Let $k_M$ be the circle with center $M$ and radius $MP$ , and let $k_N$ be the circle with center $N$ and radius $NP$ . Let $A$ and $B$ be the common points of $k_M$ and the line $MN$ , and let $C$ and $D$ be the common points of $k_N$ and the line $MN$ with with $C$ between $A$ and $B$ . Prove that the line $PC$ bisects the angle $\angle APB$ .