MathNet 2017-part-03 — 176 problems (EN–VI) Question 85

Let $A B C D E$ be a convex pentagon such that $A B = B C = C D$, $\angle E A B = \angle B C D$, and $\angle E D C = \angle C B A$. Prove that the perpendicular line from $E$ to $B C$ and the line segments $A C$ and $B D$ are concurrent.