Question 9
G3 (TUR). The incircle of $ABC$ touches $BC$, $CA$, and $AB$ at $D$, $E$, and $F$ respectively. $X$ is a point inside $ABC$ such that the incircle of $XBC$ touches $BC$ at $D$ also, and touches $CX$ and $XB$ at $Y$ and $Z$, respectively. Prove that $EFZY$ is a cyclic quadrilateral.