IrMO 2012 Problem 7

Consider a triangle $ABC$ with $|AB|\neq |AC|$ . The angle bisector of the angle $CAB$ intersects the circumcircle of $\triangle ABC$ at two points $A$ and $D$ . The circle of center $D$ and radius $|DC|$ intersects the line $AC$ at two points $C$ and $B'$ . The line $BB'$ intersects the circumcircle of $\triangle ABC$ at $B$ and $E$ . Prove that $B'$ is the orthocenter of $\triangle AED$ .