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

Identifier:  imarina:9262320

Handle: https://hdl.handle.net/20.500.11797/imarina9262320

Authors:  Herrera, Blas; Tran, Quang Hung

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 Thébault’s theorem.We establish a link between the radical center of the four spheres, the insphere, and the Monge point of a tetrahedron.