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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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

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spelling	doaj-ac82838cabd546f7a307a14a45d3082b2020-11-24T23:27:56ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122242343010.1155/S0161171299224234The Gergonne point generalized through convex coordinatesJ. N. Boyd0P. N. Raychowdhury1Department of Mathematical Sciences, Virginia Commonwealth University , Richmond 23284-2014, Virginia, USADepartment of Mathematical Sciences, Virginia Commonwealth University , Richmond 23284-2014, Virginia, USAThe 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.http://dx.doi.org/10.1155/S0161171299224234Convex (barycentric) coordinatescevianGergonne pointincircleCeva's theorem.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	J. N. Boyd P. N. Raychowdhury
spellingShingle	J. N. Boyd P. N. Raychowdhury The Gergonne point generalized through convex coordinates International Journal of Mathematics and Mathematical Sciences Convex (barycentric) coordinates cevian Gergonne point incircle Ceva's theorem.
author_facet	J. N. Boyd P. N. Raychowdhury
author_sort	J. N. Boyd
title	The Gergonne point generalized through convex coordinates
title_short	The Gergonne point generalized through convex coordinates
title_full	The Gergonne point generalized through convex coordinates
title_fullStr	The Gergonne point generalized through convex coordinates
title_full_unstemmed	The Gergonne point generalized through convex coordinates
title_sort	gergonne point generalized through convex coordinates
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1999-01-01
description	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.
topic	Convex (barycentric) coordinates cevian Gergonne point incircle Ceva's theorem.
url	http://dx.doi.org/10.1155/S0161171299224234
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The Gergonne point generalized through convex coordinates

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