International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 423-430
doi:10.1155/S0161171299224234
The Gergonne point generalized through convex coordinates
J.N. Boyd
and P.N. Raychowdhury
Department of Mathematical Sciences, Virginia Commonwealth University , Richmond 23284-2014, Virginia, USA
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.