OMM 2006 Problem 5

Let $ABC$ be an acute triangle , with altitudes $AD,BE$ and $CF$ . Circle of diameter $AD$ intersects the sides $AB,AC$ in $M,N$ respevtively. Let $P,Q$ be the intersection points of $AD$ with $EF$ and $MN$ respectively. Show that $Q$ is the midpoint of $PD$ .