IR-TST 2009 Problem 9

In triangle $ABC$ , $D$ , $E$ and $F$ are the points of tangency of incircle with the center of $I$ to $BC$ , $CA$ and $AB$ respectively. Let $M$ be the foot of the perpendicular from $D$ to $EF$ . $P$ is on $DM$ such that $DP = MP$ . If $H$ is the orthocenter of $BIC$ , prove that $PH$ bisects $EF$ .