KöMaL 2009 C974

ABCD is a cyclic trapezium. Diagonal $BD$ is extended beyond vertex $D$ by the length of the leg and the point $L$ is obtained. $K$ is the point on diagonal $AC$ whose distance from $C$is equal to the leg. Prove that the areas of the rectangles formed by the line segments $AB$and $CD$ and the line segments $AK$ and $BL$ are equal.