Problem #NZO-000004

Problem

Let $A B C D$ be a trapezium such that $A B$ is parallel to $C D$ . Let $E$ be the intersection of diagonals $A C$ and $B D$ . Suppose that $A B = B E$ and $A C = D E$ . Prove that the internal angle bisector of $∠ B A C$ is perpendicular to $A D$ .

To see the solution register and get verified.