Geodesic
A Property of the Fermat-Torricelli Point for Tetrahedra and a new Characterization for Isosceles Tetrahedra
Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 187-193 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M14, 51M20, 51M16
Mots-clés : Fermat-Torricelli point, angle bisector, isosceles tetrahedra 
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     author = {A. N. Zachos },
     title = {A {Property} of the {Fermat-Torricelli} {Point} for {Tetrahedra} and a new {Characterization} for {Isosceles} {Tetrahedra}},
     journal = {Journal for geometry and graphics},
     pages = {187--193},
     year = {2023},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a6/}
}
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A. N. Zachos . A Property of the Fermat-Torricelli Point for Tetrahedra and a new Characterization for Isosceles Tetrahedra. Journal for geometry and graphics, Tome 27 (2023) no. 2, pp. 187-193. http://geodesic.mathdoc.fr/item/JGG_2023_27_2_JGG_2023_27_2_a6/