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In this paper we give a completely synthetic proof of the TCC-perspectortheorem, 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 theisogonal conjugate $\gamma(Q)$, where $Q$ is the complement of the isotomicconjugate $P'$ of the point $P$.

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