Let O and H be the circumcenter and the orthocenter, respectively, of an acute triangle ABC. Points D and E are chosen from sides AB and AC, respectively, such that A, D, O, E are concyclic. Let P be a point on the circumcircle of triangle ABC. The line passing P and parallel to OD intersects AB at point X, while the line passing P and parallel to OE intersects AC at Y. Suppose that the perpendicular bisector of HP does not coincide with XY, but intersect XY at Q, and that points A, Q lies on the different sides of DE. Prove that ∠EQD=∠BAC. Proposed by Shuang-Yen Lee geometrymoving pointsTaiwan