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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299224234 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558125367951360 |
|---|---|
| author | J. N. Boyd P. N. Raychowdhury |
| author_facet | J. N. Boyd P. N. Raychowdhury |
| author_sort | J. N. Boyd |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ac82838cabd546f7a307a14a45d3082b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ac82838cabd546f7a307a14a45d3082b2025-02-03T01:33:16ZengWileyInternational 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. |
| 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. |
| title | 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_short | The Gergonne point generalized through convex coordinates |
| title_sort | gergonne point generalized through convex coordinates |
| topic | Convex (barycentric) coordinates cevian Gergonne point incircle Ceva's theorem. |
| url | http://dx.doi.org/10.1155/S0161171299224234 |
| work_keys_str_mv | AT jnboyd thegergonnepointgeneralizedthroughconvexcoordinates AT pnraychowdhury thegergonnepointgeneralizedthroughconvexcoordinates AT jnboyd gergonnepointgeneralizedthroughconvexcoordinates AT pnraychowdhury gergonnepointgeneralizedthroughconvexcoordinates |