MathNet 2018-part-06 — 181 problems (EN–VI) Question 42

Let $ABCDE$ be a convex pentagon with $AB = BC = CD$, $\angle EAB = \angle BCD$, and $\angle EDC = \angle CBA$. Prove that the line through $E$ perpendicular to $BC$ and the segments $AC$ and $BD$ are concurrent.