NZ-NZMO 2020 Problem 2

Let $ABCD$ be a square and let $X$ be any point on side $BC$ between $B$ and $C$ . Let $Y$ be the point on line $CD$ such that $BX = YD$ and $D$ is between $C$ and $Y$ . Prove that the midpoint of $XY$ lies on diagonal $BD$ .