OIM 2022 Problem 1

Given is an equilateral triangle $ABC$ with circumcenter $O$ . Let $D$ be a point on to minor arc $BC$ of its circumcircle such that $DB>DC$ . The perpendicular bisector of $OD$ meets the circumcircle at $E, F$ , with $E$ lying on the minor arc $BC$ . The lines $BE$ and $CF$ meet at $P$ . Prove that $PD \perp BC$ .