Synthetic foundations of cevian geometry, IV: the TCC-perspector theorem

Abstract

In this paper we give a completely synthetic proof of the TCC-perspector theorem, that the isogonal conjugate $\gamma(H)$ of the generalized orthocenter $H$ (defined in Part III of this series of papers), with respect to a triangle $ABC$ and a point $P$, is the perspector of the tangential triangle of $ABC$ and the circumcevian triangle (both with respect to the circumcircle) of the isogonal conjugate $\gamma(Q)$, where $Q$ is the complement of the isotomic conjugate $P'$ of the point $P$.