Let P be a point; A', B', C' its cevian traces. Let Ab, Ac be the midpoints of AB', AC' and define analogously Bc, Ba, Ca, Cb. Let A1, B1, C1 lbe the midpoints of AA', BB', CC'; A2, B2, C2 the midpoints of BcCb, CaAc, AbBa. The lines A1A2, B1B2, C1C2 concur.