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Journal for Geometry and Graphics 27 (2023), No. 2, 187--193
Copyright Heldermann Verlag 2023

A Property of the Fermat-Torricelli Point for Tetrahedra and a new Characterization for Isosceles Tetrahedra

Anastasios N. Zachos
Dept. of Mathematics, University of Patras, Greece


If the Fermat-Torricelli point $A_0$ is strictly inside a tetrahedron $A_1A_2A_3A_4$, we prove that the angle bisectors of $\angle A_iA_0A_j$, for $i \neq j$, $i,j = 1,2,3,4$ form three bisecting lines that meet perpendicular at $A_0$. From this, we derive a new characterization of isosceles tetrahedra.

Keywords: Fermat-Torricelli point, angle bisector, isosceles tetrahedra.

MSC: 51M14; 51M20, 51M16.

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