OFM 2022 J3

Let $\triangle ABC$ a triangle, and $D$ the intersection of the angle bisector of $\angle BAC$ and the perpendicular bisector of $AC$ . the line parallel to $AC$ passing by the point $B$ , intersect the line $AD$ at $X$ . the line parallel to $CX$ passing by the point $B$ , intersect $AC$ at $Y$ . $E = (AYB) \cap BX$ . prove that $C$ , $D$ and $E$ collinear.