IR-TST 2012 Problem 2

Consider $\omega$ is circumcircle of an acute triangle $ABC$ . $D$ is midpoint of arc $BAC$ and $I$ is incenter of triangle $ABC$ . Let $DI$ intersect $BC$ in $E$ and $\omega$ for second time in $F$ . Let $P$ be a point on line $AF$ such that $PE$ is parallel to $AI$ . Prove that $PE$ is bisector of angle $BPC$ .

Proposed by Mr.Etesami