# Diagonals in 4-teral

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• September 5th 2010, 04:17 AM
atreyyu
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 $AC=BD$.

I'm stuck. (Headbang) Ideas, clues ,please.
• September 5th 2010, 10:49 AM
Pim
$AC = BD$ implies $ABCD$ is a rhombus
Also, drawing pictures helps. Supplying a picture also shows that you put some effort in trying this question yourself.