Let $AG, CH$ be the angle bisectors of a triangle $ABC$. It is known that one of the intersections of the circles of triangles $ABG$ and $ACH$ lies on the side $BC$. Prove that the angle $BAC$ is $60 ^o$
Problem
Source: 2006 Estonia National Olympiad Final Round grade 10 p3
Tags: geometry, angle bisector, Angle Chasing, circumcircle