IR-TST 2002 Problem 13

Let $ABC$ be a triangle. The incircle of triangle $ABC$ touches the side $BC$ at $A^{\prime}$ , and the line $AA^{\prime}$ meets the incircle again at a point $P$ . Let the lines $CP$ and $BP$ meet the incircle of triangle $ABC$ again at $N$ and $M$ , respectively. Prove that the lines $AA^{\prime}$ , $BN$ and $CM$ are concurrent.