Let I be the incenter; Ia, Ib, Ic the excenters; r a line through I; I'a, I'b, I'c the reflections of Ia, Ib, Ic on r. The circles {I'aBC}, {I'bCA}, {I'cAB} have a common point and the same happens to the circles {AI'bI'c}, {BI'cI'a}, {CI'aI'b}.