Question 56
Given an acute triangle $ABC$ inscribed in $(O)$ with $\angle A = 60^\circ$ and symmedian point $L$. The tangents at $B, C$ of $(O)$ intersect $CA, AB$ at $E, F$. Prove that the line $OL$, two circumcircles of triangles $AEF$ and $BOC$ pass through the same point.