Let I, Ea, Eb, Ec be the incenter and the excenters of ABC. Let Iaa, Iab, Iac be the excenters of IBC opposite to the angles I, B, C. Define analogously Ibb, Ibc, Iba, Icc, Ica, Icb. Let Ha, Hb, Hc be the orthocenters of the triangles IaIabIac, IbIbcIba, IcIcaIcb. The lines AHa, BHb, CHc concur.