KöMaL 2012 C1122

The angle bisector of angle BAC of a triangle ABC intersects side $BC$ at $A_1$. Let the centres of the circumscribed circles of triangles ABC , ABA $_1$, ACA $_1$ be $O$, $O_1$, $O_2$, respectively. Prove that triangle $OO_1 O_2$ is isosceles.