Let ABC be a scalene triangle with incenter I and circumcircle ω. The internal and external bisectors of angle ∠BAC intersect BC at D and E, respectively. Let M be the point on segment AC such that MC=MB. The tangent to ω at B meets MD at S. The circumcircles of triangles ADE and BIC intersect each other at P and Q. If AS meets ω at a point K other than A, prove that K lies on PQ.Proposed by Alexandru Lopotenco (Moldova) geometrygeometry proposedcircle intersections