US-TST 2010 Problem 4

Let $ABC$ be a triangle. Point $M$ and $N$ lie on sides $AC$ and $BC$ respectively such that $MN || AB$ . Points $P$ and $Q$ lie on sides $AB$ and $CB$ respectively such that $PQ || AC$ . The incircle of triangle $CMN$ touches segment $AC$ at $E$ . The incircle of triangle $BPQ$ touches segment $AB$ at $F$ . Line $EN$ and $AB$ meet at $R$ , and lines $FQ$ and $AC$ meet at $S$ . Given that $AE = AF$ , prove that the incenter of triangle $AEF$ lies on the incircle of triangle $ARS$ .