Question 42
In the triangle $ABC$, $I$ is the incenter and $M$ is the midpoint of the arc $BC$ of the circumcircle of $ABC$ that doesn't contain $A$. $X$ is a point on the external angle bisector of $\angle BAC$. The line $BX$ meets the circumcircle of $BIC$ at $T$ for the second time. The point $Y \ne A$ is on the circumcircle of $AXC$ such that $MA = MY$. Prove that $TC \parallel AY$.
