Problem

Source: ELMO 2022 P4

Tags: geometry, similar triangles, ELMO 2022, Elmo, water balloon



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