ELMO 2022 Problem 4

Let $ABCDE$ be a convex pentagon such that $\triangle ABE$ , $\triangle BEC$ , and $\triangle EDB$ are similar (with vertices in order). Lines $BE$ and $CD$ intersect at point $T$ . Prove that line $AT$ is tangent to the circumcircle of $\triangle ACD$ .

Holden Mui