Fixed points and fixed lines of Ceva collineations

摘要

In the plane of a triangle ABC, the U-Ceva collineation maps points to points and lines to lines.  If U is a triangle center other than the incenter, then the U-Ceva collineation has three distinct fixed points F_1, F_2, F_3 and three distinct fixed lines F_2F_3,F_3F_1,F_1F_2, these being the trilinear polars of F_1, F_2,F_3.  When U is the circumcenter, the fixed points are the symmedian point and the isogonal conjugates of the points in which the Euler line intersects the circumcircle.