In the acute triangle ABC the orthocenter H and the center of the circumscribed circle O were noted. The line AO intersects the side BC at the point D. A perpendicular drawn to the side BC at the point D intersects the heights from the vertices B and C of the triangle ABC at the points X and Y respectively. Prove that the center of the circumscribed circle ΔHXY is equidistant from the points B and C.(Danilo Hilko)
geometrycircumcircleequal segments