Let D,E,F be the points of tangency of the incircle of a given triangle ABC with sides BC,CA,AB, respectively. Denote by I the incenter of ABC, by M the midpoint of BC and by G the foot of the perpendicular from M to line EF. Prove that the line ID is tangent to the circumcircle of the triangle MGI. JBMOJBMO Shortlistgeometrycircumcircle