An Analogue of Thébault's Theorem Linking the Radical Center of Four Spheres with the Insphere and the Monge Point of a Tetrahedron

Year 2022, Volume: 15 Issue: 1, 75 - 78, 30.04.2022

Blas Herrera Quang Hung Tran

https://doi.org/10.36890/iejg.957190

Cited By: 1

Abstract

In 1953, Victor Thébault conjectured a link between the altitudes of a tetrahedron and the radical center of the four spheres with the centers at the vertices of this tetrahedron and the corresponding tetrahedron altitudes as radii. This conjecture was proved in 2015. In this paper, we propose an analogue of Th\'{e}bault's theorem. We establish a link between the radical center of the four spheres, the insphere, and the Monge point of a tetrahedron.

Keywords

Solid geometry, Thébault's theorem, tetrahedron, radical center of spheres, Monge point, insphere

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