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 PaA", PbB", PcC" bound a triangle A*B*C* perspective with ABC.