In Triangle ABC, points P and Q lie on sides AB and AC, respectively, such that the circumcircle of Triangle APQ is tangent to side BC at D. Let EE lie on side BCBC such that BD ≅ EC. Line DP intersects the circumcircle of Triangle CDQ again at X, and line DQ intersects the circumcircle of Triangle BDP again at Y. Prove that D,E,X and Y are concyclic.

It would be nice if someone could post diagram and solution.

hellothere Jun 19, 2021