ISL 1995 G3

The incircle of triangle $\triangle ABC$ touches the sides $BC$ , $CA$ , $AB$ at $D, E, F$ respectively. $X$ is a point inside triangle of $\triangle ABC$ such that the incircle of triangle $\triangle XBC$ touches $BC$ at $D$ , and touches $CX$ and $XB$ at $Y$ and $Z$ respectively. Show that $E, F, Z, Y$ are concyclic.