The perpendicular from A to AB cuts BC at Ca, and the perpendicular from A to AC cuts BC at Ba. Define analogously Ac, Bc, Cb, Ab. Let La, Lb, Lc be the midpoints of AbAc, BcBa, CaCb. Let Ma, Mb, Mc be the midpoints of BaCa, CbAb, AcBc. Then MaLa, MbLb, McLc concur.