Let I be the incenter; Na, Nb, Nc the ninecenters of IBC, ICA, IAB. Let Nab, Nac be the orthogonal projections of Na on IB, Ic. Define analogously Nba, Nbc, Nca, Ncb. The triangles NaNabNac, NbNbcNba, NcNcaNcb have the same circumcenter I.