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arXiv · 2101.02592

Arrangement of Central Points on the Faces of a Tetrahedron

Stanley Rabinowitz
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Abstract

We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of the tetrahedron. Using a computer, we determine when any of 16 conditions occur (such as the four centers being coplanar). A typical result is: The lines from each vertex of a circumscriptible tetrahedron to the Gergonne points of the opposite face are concurrent.

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Stanley Rabinowitz. 2021-01-06. Arrangement of Central Points on the Faces of a Tetrahedron. https://arxiv.org/abs/2101.02592

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