Question 92
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 $KM \perp DL$.