IGO 2016-P5

Let the circles ω and ωintersect in points A and B. Tangent to circle ω at A intersects ωin C and tangent to circle ωat A intersects ω in D. Suppose that the internal bisector of ∠CAD intersects ω and ωat E and F, respectively, and the external bisector of ∠CAD intersects ω and ωin X and Y, respectively. Prove that the perpendicular bisector of XY is tangent to the circumcircle of triangle BEF