ILL 1978 Problem 42

$A,B,C,D,E$ are points on a circle $O$ with radius equal to $r$ . Chords $AB$ and $DE$ are parallel to each other and have length equal to $x$ . Diagonals $AC,AD,BE, CE$ are drawn. If segment $XY$ on $O$ meets $AC$ at $X$ and $EC$ at $Y$ , prove that lines $BX$ and $DY$ meet at $Z$ on the circle.