In the acute-angled triangle ABC, the point F is the foot of the altitude from A, and P is a point on the segment AF. The lines through P parallel to AC and AB meet BC at D and E, respectively. Points X=A and Y=A lie on the circles ABD and ACE, respectively, such that DA=DX and EA=EY.
Prove that B,C,X, and Y are concyclic. geometryarc midpointcyclic quadrilateralISL 2022