Question 14
G8 (RUS) Points $A,B,C$ divide the circumcircle $\Omega$ of the triangle $ABC$ into three arcs. Let $X$ be a variable point on the arc $AB$, and let $O_1,O_2$ be the incenters of the triangles $CAX$ and $CBX$. Prove that the circumcircle of the triangle $XO_1O_2$ intersects $\Omega$ in a fixed point.