Given △ABC and points D and E at the line BC, furthermore there are points X and Y inside △ABC. Let P be the intersection of line AD and XE, and Q be the intersection of line AE and YD.
If there exist a circle that passes through X,Y,D,E, and
∠BXE+∠BCA=∠CYD+∠CBA=180∘
Prove that the line BP, CQ, and the perpendicular bisector of BC intersect at one point. geometryIndonesiaregional olympiadRMO