Let ABC be a triangle with incenter I and circumcircle Ω. A point X on Ω which is different from A satisfies AI=XI. The incircle touches AC and AB at E,F, respectively. Let Ma,Mb,Mc be the midpoints of sides BC,CA,AB, respectively. Let T be the intersection of the lines MbF and McE. Suppose that AT intersects Ω again at a point S.Prove that X,Ma,S,T are concyclic.Proposed by ltf0501 and Li4 geometryincentercircumcircle