Question 57
Let $H$ be the orthocentre and $G$ be the centroid of acute-angled triangle $\triangle ABC$ with $AB \neq AC$. The line $AG$ intersects the circumcircle of $\triangle ABC$ at $A$ and $P$. Let $P'$ be the reflection of $P$ in the line $BC$. Prove that $\angle CAB = 60^\circ$ if and only if $HG = GP'$.