Question 67
Let $O$ be the circumcentre of $\triangle ABC$. Suppose $AB \gt AC \gt BC$. Let $D$ be a point on the minor arc $BC$ such that $AD$ is not a diameter of the circumcircle of $\triangle ABC$. Let $E$ and $F$ be points on $AD$ such that $AB \perp OE$ and $AC \perp OF$. Let $P$ be the intersection of $BE$ and $CF$. If $PB = PC + PO$, then prove that $\angle BAC = 30^\circ$.