Let ABC be a triangle and A'B'C' the cevian triangle of P = I
Ab = the orthogonal projection of A' on the parallel to BB' through A
Ac = the orthogonal projection of A' on the parallel to CC' through A
Similarly (cyclically) Bc, Ba and Ca,Cb.
Conjecture: ABC and The triangle bounded by the Euler lines of AAbAc, BBcBa, CCaCb are parallelogic.
Antreas P. Hatzipolakis. 7 September 2014
Generalization: Hyacinthos #22570