Let ABC be a triangle. Let T be the point of tangency of the circumcircle of triangle ABC and the A-mixtilinear incircle. The incircle of triangle ABC has center I and touches sides BC,CA and AB at points D,E and F, respectively. Let N be the midpoint of line segment DF. Prove that the circumcircle of triangle BTN, line TI and the perpendicular from D to EF are concurrent.Proposed by Diaconescu Tashi, Romania geometrykomalmixtilinear incircle