Let Pa, Pb, Pc  be the intersections between the line OI (O circumcenter, I incenter) and the sides; A", B", C" the orthogonal projections of Pa, Pb, Pc on the cevians of O; A', B', C' the midpoints of the sides of ABC. The lines A'A", B'B", C'C" concur at the Feuerbach point F.