MathNet 2009-part-01 — 175 problems (EN–VI) Question 135

For a convex pentagon $ABCDE$, $AB = DE$, $BC = EA$, $AB \neq EA$, and $B$, $C$, $D$, $E$ are concyclic. Prove that $A$, $B$, $C$, $D$ are concyclic if and only if $AC = AD$. (Posed by Xiong Bin)