Let ABC be a triangle such that AB=AC and ∠BAC is obtuse. Point O is the circumcenter of triangle ABC, and M is the reflection of A in BC. Let D be an arbitrary point on line BC, such that B is in between D and C. Line DM cuts the circumcircle of ABC in E,F. Circumcircles of triangles ADE and ADF cut BC in P,Q respectively. Prove that DA is tangent to the circumcircle of triangle OPQ. geometrycircumcirclegeometric transformationreflection