AT-OEMO-REG 2021 Problem 2

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 $BDE$ .

(Karl Czakler)