AT-OEMO-FED1 2021 Problem 2

Let $ABC$ denote a triangle. The point $X$ lies on the extension of $AC$ beyond $A$ , such that $AX = AB$ . Similarly, the point $Y$ lies on the extension of $BC$ beyond $B$ such that $BY = AB$ . Prove that the circumcircles of $ACY$ and $BCX$ intersect a second time in a point different from $C$ that lies on the bisector of the angle $\angle BCA$ .

(Theresia Eisenkölbl)