Let ABC be a triangle with incircle touching BC,CA,AB at D,E,F, respectively. Let O and M be its circumcenter and midpoint of BC. Suppose that circumcircles of AEF and ABC intersect at X for the second time. Assume Y=X is on the circumcircle of ABC such that OMXY is cyclic. Prove that circumcenter of DXY lies on BC.Proposed by tenplusten. geometrycircumcirclesharky-deviltangency