Question 2
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 $BC$.