NL-BXMO-TST 2011 Problem 2

In an acute triangle $ABC$ the angle $\angle C$ is greater than $\angle A$ . Let $E$ be such that $AE$ is a diameter of the circumscribed circle $\Gamma$ of \vartriangle ABC. Let $K$ be the intersection of $AC$ and the tangent line at $B$ to $\Gamma$ . Let $L$ be the orthogonal projection of $K$ on $AE$ and let $D$ be the intersection of $KL$ and $AB$ . Prove that $CE$ is the bisector of $\angle BCD$ .