Question 189
Let $I$ be the incenter of the triangle $ABC$. Let $X$ lie on segment $AB$, such that $\angle AIX = 90^\circ$. The circumcircle of triangle $BIX$ intersects the circumcircle of triangle $ABC$ at point $Y \neq B$ lying on the same side of $AB$ as point $C$. Prove that $YX$ is the bisector of angle $AYB$.