Let \(AA'BCC'B'\) be a convex cyclic hexagon such that \(AC\) is tangent to the incircle of the triangle \(A'B'C'\), and \(A'C'\) is tangent to the incircle of the triangle \(ABC\). Let the lines \(AB\) and \(A'B'\) meet at \(X\) and let the lines \(BC\) and \(B'C'\) meet at \(Y\).

Prove that if \(XBYB'\) is a convex quadrilateral, then it has an incircle.