Question 13
Let $ABC$ be a triangle with $AB = AC$. A circle $\Gamma$ lies outside triangle $ABC$ and is tangent to line $AC$ at $C$. Point $D$ lies on $\Gamma$ such that the circumcircle of triangle $ABD$ is internally tangent to $\Gamma$. Segment $AD$ meets $\Gamma$ again at $E$. Prove that $BE$ is tangent to $\Gamma$.