Let I, Ea, Eb, Ec be the incenter and the excenters; r a line through I and A', B', C' the orthogonal projections of A, B, C on r. Let A*, B*, C* be the midpoints of AA', BB', CC' and Ma, Mb, Mc the midpoints of  A*Ea, B*Eb, C*Ec. The triangles ABC, MaMbMc are orthologic.