Abstract.
The Gergonne center of a triangle is the intersection of the cevians through the points where the incircle touches the sides. This does not admit a direct generalization to tetrahedra since the cevians of a tetrahedron through the points where the insphere touches the faces are not necessarily concurrent. This article introduces an alternative definition of the Gergonne center that coincides with the previous definition for the triangle and that admits a generalization to tetrahedra. The same is done for the Nagel center.
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Received 4 February 2000; revised 1 May 2000.
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Hajja, M., Walker, P. The Gergonne and Nagel centers of a tetrahedron. J.Geom. 75, 106–112 (2002). https://doi.org/10.1007/s00022-002-1490-0
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DOI: https://doi.org/10.1007/s00022-002-1490-0