Fixed Points and Fixed Lines of Ceva Collineations

Clark Kimberling
2007 Forum Geometricorum   unpublished
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 F1, F2, F3 and three distinct fixed lines F2F3, F3F1, F1F2, these being the trilinear polars of F1, F2, F3. 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 circum-circle.