Let I be the incenter; A', B', C' its cevian traces. Let Oa, Obc, Ocb be the circumcenters of IBC, IBC', IC'B and define analogously Ob, Oca, Oac, Oc, Oab, Oba.
1) The radical center of the circles {OaObcOcb}, {ObOcaOac}, {OcOabOba} is the midpoint X between I and the circumcenter O of ABC
2) Let Ja, Jb, Jc be the circumcenters of OaObcOcb, ObOcaOac, OcOabOba. The lines AJa, BJb, CJc concur.