Question 53
Let $ABC$ be an isosceles triangle with $AC = BC$ and circumcircle $k$. The point $D$ lies on the shorter arc of $k$ over the chord $BC$ and is different from $B$ and $C$. Let $E$ denote the intersection of $CD$ and $AB$.
Prove that the line through $B$ and $C$ is a tangent of the circumcircle of the triangle $BDE$.
Prove that the line through $B$ and $C$ is a tangent of the circumcircle of the triangle $BDE$.