Concyclicity Associated to a Radical Axis

Consider two circles with centers $A$ and $B$. Call $A'$, $A''$ the two intersections of the line $AB$ and the circle centered at $A$. Similarly, construct $B'$, $B''$. Call $X$ and $Y$ the intersections of circles $(A)$, $(B)$ with another circle passing through $A''$, $B''$. Let another circle passing through $A''$, $B''$ be intersected by both circles $(A)$, $(B)$ at $Z$, $W$, respectively.

Prove that $XYWZ$ is cyclic.