Let ABC be an obtuse triangle with ∠A>∠B>∠C, and let M be a midpoint of the side BC. Let D be a point on the arc AB of the circumcircle of triangle ABC not containing C. Suppose that the circle tangent to BD at D and passing through A meets the circumcircle of triangle ABM again at E and BD=BE. ω, the circumcircle of triangle ADE, meets EM again at F. Prove that lines BD and AE meet on the line tangent to ω at F. geometrycircumcircletangent