Let A1B1C1 be the cevian triangle of P. The circle {A1B1C1} cuts the sides of A1B1C1 at A2, B2, C2; the cevians of P at A3, B3, C3; and the lines AA2, BB2, CC2 at A4, B4, C4. The lines A1A4, B1B4, C1C4 concur, and the lines A2A3, B2B3, C2C3 concur too.