
Diagonals in 4teral
In a convex quadrilateral $\displaystyle ABCD$ points $\displaystyle X$ and $\displaystyle Y$ are center of $\displaystyle AB$ and $\displaystyle CD$ respectively, while diagonals meet at $\displaystyle E$. Show that the line containing the bisector of angle $\displaystyle BEC$ is perpendicular to line $\displaystyle XY$ iff $\displaystyle AC=BD$.
I'm stuck. (Headbang) Ideas, clues ,please.

$\displaystyle AC = BD$ implies $\displaystyle ABCD$ is a rhombus
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