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Journal for Geometry and Graphics 09 (2005), No. 1, 037--041
Copyright Heldermann Verlag 2005

Equifaciality of Tetrahedra whose Incenter and Fermat-Torricelli Center Coincide

Mowaffaq Hajja
Dept. of Mathematics, Yarmouk University, Irbid, Jordan

Peter Walker
Dept. of Mathematics and Statistics, American University, P. O. Box 26666, Sharjah, United Arab Emirates

We show that if the incenter and the Fermat-Torricelli center of a tetrahedron coincide, then the tetrahedron is equifacial (or isosceles) in the sense that all its faces are congruent. The proof is intended to replace the incorrect proof given in a previous paper of the authors [Internat. J. Math. Ed. Sci. Tech. 32 (2001) 501--508] for the same statement.

Keywords: Barycentric coordinates, Fermat-Torricelli center, isosceles tetrahedron, equifacial tetrahedron.

MSC: 51M04; 51M20, 52B10

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