923Crux 2830, proposed by D. J. Smeenk, Zaltbommel, the Netherlands
Suppose thatΓ(O, R)is the circumcircle of triangleABC. Suppose that
sideABis fixed and thatCvaries onΓ(always on the same side ofAB).
Suppose thatIa,Ib,Icare the centers of the excircles of triangleABC
oppositeA,B,Crespectively. IfΩis the center of the circumcircle of
triangleIaIbIc, determine the locus ofΩasCvaries.