MK-MO 2007 Problem 2

In a trapezoid $ABCD$ with a base $AD$ , point $L$ is the orthogonal projection of $C$ on $AB$ , and $K$ is the point on $BC$ such that $AK$ is perpendicular to $AD$ . Let $O$ be the circumcenter of triangle $ACD$ . Suppose that the lines $AK , CL$ and $DO$ have a common point. Prove that $ABCD$ is a parallelogram.