ELMO SL 2010 G2

Given a triangle $ABC$ , a point $P$ is chosen on side $BC$ . Points $M$ and $N$ lie on sides $AB$ and $AC$ , respectively, such that $MP \parallel AC$ and $NP \parallel AB$ . Point $P$ is reflected across $MN$ to point $Q$ . Show that triangle $QMB$ is similar to triangle $CNQ$ .

Brian Hamrick.