Question 80
In the acute triangle $ABC$, angle $C$ is greater than angle $A$. Choose $E$ so that $AE$ is a diameter of the circumcircle $\Gamma$ of triangle $ABC$. Let $K$ be the intersection of $AC$ and the tangent to $\Gamma$ at $B$. Let $L$ be the foot of the perpendicular from $K$ to $AE$, and let $D$ be the intersection of $KL$ and $AB$. Prove that $CE$ bisects $\angle BCD$.
