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
mhajja@yu.edu.jo
Peter Walker
Dept. of Mathematics and Statistics, American University, P. O. Box 26666, Sharjah, United Arab Emirates
peterw@aus.ac.ae
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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