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 $P^{\prime }$ of the point $P$.

arXiv comment29 pages, 6 figures

References in corpus (1)

• Vertex positions of the generalized orthocenter and a related elliptic curve

Cited by in corpus (1)

• A cevian locus and the geometric construction of a special elliptic curve