In the circle Ω the hexagon ABCDEF is inscribed. It is known that the point D divides the arc BC in half, and the triangles ABC and DEF have a common inscribed circle. The line BC intersects segments DF and DE at points X and Y and the line EF intersects segments AB and AC at points Z and T respectively. Prove that the points X,Y,T and Z lie on the same circle.Proposed by D. Brodsky Kvantgeometryporismhexagon