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International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 423-430
http://dx.doi.org/10.1155/S0161171299224234

The Gergonne point generalized through convex coordinates

Department of Mathematical Sciences, Virginia Commonwealth University , Richmond 23284-2014, Virginia, USA

Received 27 May 1997; Revised 20 October 1997

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Gergonne point of a triangle is the point at which the three cevians to the points of tangency between the incircle and the sides of the triangle are concurrent. In this paper, we follow Koneĉný [7] in generalizing the idea of the Gergonne point and find the convex coordinates of the generalized Gergonne point. We relate these convex coordinates to the convex coordinates of several other special points of the triangle. We also give an example of relevant computations.