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. The lines joining the incenter and the circumcenter of the triangles IaIabIac, IbIbcIba, IcIcaIcb go throughr Ea, Eb, Ec and concur.