Problem

Source: 2024 CTST P17

Tags: geometry



$ABCDE$ is a convex pentagon with $BD=CD=AC$, and $B$, $C$, $D$, $E$ are concyclic. If $\angle BAC+\angle AED=180^{\circ}$ and $\angle DCA=\angle BDE$, prove that $AB=DE$ or $AB=2AE$.