Let Ω be the circumcircle of triangle ABC. Suppose that X is a point on the segment AB with XB=XC, and the angle bisector of ∠BAC intersects BC and Ω at D, M, respectively. If P is a point on BC such that AP is tangent to Ω and Q is a point on DX such that CQ is tangent to Ω, show that AB, CM, PQ are concurrent. geometrycircumcircleconcurrent