Question 150
Let $ABCD$ be a quadrilateral inscribed in a circle $\Gamma$ such that $AB = BC = CD$. Let $M$ and $N$ be the midpoints of $AD$ and $AB$ respectively. The line $CM$ meets $\Gamma$ again at $E$. Prove that the tangent at $E$ to $\Gamma$, the line $AD$ and the line $CN$ are concurrent.