Isogonal Conjugates and the Incenter
Points P and P' are Isogonal Conjugates when the cevians from the same vertex for P and P'
make equal angles with the angle bisector of that vertex.
The incenter is its own conjugate.
If F is the conjugate transformation, F(P) = P' and F(P') = P and F(I) = I. The incenter is a fixed point of the transformation.