Question 132
Given is an equilateral triangle $ABC$ with circumcenter $O$. Let $D$ be a point on the minor arc $BC$ of its circumcircle such that $DB \gt DC$. 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 $PD \perp BC$.