IR-TST 2017 Problem 18

In triangle $ABC$ let $O$ and $H$ be the circumcenter and the orthocenter. The point $P$ is the reflection of $A$ with respect to $OH$ . Assume that $P$ is not on the same side of $BC$ as $A$ . Points $E,F$ lie on $AB,AC$ respectively such that $BE=PC \ , CF=PB$ . Let $K$ be the intersection point of $AP,OH$ . Prove that $\angle EKF = 90 ^{\circ}$ Proposed by Iman Maghsoudi