Let PaPbPc the cevian triangle of a point P. The circles (Pa, PaPb) – centered at Pa and going through Pb -, (Pb, PbPb), (Pc, PcPa) have radical center X and the circles (Pa, PaPc), (Pb, PbPa), (Pc, PcPb) have radical center Y. The midpoint between X, Y is the ninecenter N of PaPbPc.