Question 63
Consider an acute-angled triangle $\triangle ABC$ with $AB = AC$ and $\angle A \gt 60^\circ$. Let $O$ be the circumcenter of $\triangle ABC$. Point $P$ lies on the circumcircle of $\triangle BOC$ such that $BP \parallel AC$, and point $K$ lies on segment $AP$ such that $BK = BC$. Prove that line $CK$ bisects the arc $\widehat{BC}$ of circumcircle of $\triangle BOC$.