Diagonals in 4-teral

In a convex quadrilateral $ABCD$ points $X$ and $Y$ are center of $AB$ and $CD$ respectively, while diagonals meet at $E$. Show that the line containing the bisector of angle $BEC$ is perpendicular to line $XY$ iff $AC=BD$.
$AC = BD$ implies $ABCD$ is a rhombus