BALKAN-SL 2014 G5

Let $ABCD$ be a trapezium inscribed in a circle $k$ with diameter $AB$ . A circle with center $B$ and radius $BE$ ,where $E$ is the intersection point of the diagonals $AC$ and $BD$ meets $k$ at points $K$ and $L$ . If the line ,perpendicular to $BD$ at $E$ ,intersects $CD$ at $M$ ,prove that $KM\perp DL$ .