The Gergonne point generalized through convex coordinates

The Gergonne point generalized through convex coordinates

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...

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Bibliographic Details
Main Authors: J. N. Boyd, P. N. Raychowdhury
Format: Article
Language:English
Published: Hindawi Limited 1999-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Convex (barycentric) coordinates
cevian
Gergonne point
incircle
Ceva's theorem.
Online Access:http://dx.doi.org/10.1155/S0161171299224234
Description
Summary: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.
ISSN:0161-1712
1687-0425

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