Question 50
Let $I$ be the incenter of $\triangle ABC$ and $\omega$ be its incircle. Let $D$ be the intersection of $\omega$ with $BC$. Suppose $X$, $Y$ are points on $\omega$ such that lines $IX$, $IY$ and $AD$ are tangent to the circumcircle of $\triangle AXY$. Prove that line $XY$ bisects segment $BC$.