Question 109
The perpendicular bisector to the side $AC$ of triangle $ABC$ meets $BC$ and $AB$ at points $A_1$ and $C_1$ respectively. Let points $O$ and $O_1$ be the circumcenters of triangles $ABC$ and $A_1BC_1$ respectively. Prove that $C_1O_1$ is a tangent to the circumcircle of the triangle $ABC$.