A Construction Theorem for the Triangle Center X(222)

In this paper, we present a construction theorem for the triangle center X(222).Let ABC be a triangle with incenter I. Consider the tangents at I to the circum-circles of ABI, BCI, and CAI. By intersecting these tangents with the sidelines ofABC, we obtain three triangles CDE, AF G, and BHJ. Let their circumcircles bedenoted by ωC , ωA, and ωB , respectively. We prove that the radical center of thesethree circles coincides with X(222), which is the X(7)-Ceva conjugate of X(56).The proof is based on a characterization of the three radical axes and the geometricproperties of the Ceva conjugacy.