Original scientific paper

https://doi.org/10.31896/k.28.4

Cramer-Castillon on a Triangle's Incircle and Excircles

Dominique Laurain ; Enseeiht, Toulouse, France
Peter Moses ; Moparmatic Inc., Worcestershire, England
Dan Reznik ; Data Science Consulting, Rio De Janeiro, Brazil *

* Corresponding author.

Abstract

The Cramer-Castillon problem (CCP) consists in finding one or more polygons inscribed in a circle such that their sides pass cyclically through a list of N points. We study this problem where the points are the vertices of a triangle and the circle is either the incircle or one of the excircles. We find that (i) in each case there is always a pair of solutions (total of 8 new triangles and 24 vertices); (ii) each pair shares all Brocard geometry objects, (iii) barycentric coordinates are laden with the golden ratio; and (iv) simple operations on the barycentrics of a single vertex out of the 24 yield all other 23.

Keywords

Golden ratio; triangle; Brocard; symmedian

Hrčak ID:

324086

URI

https://hrcak.srce.hr/324086

Publication date:

20.12.2024.

Article data in other languages: croatian

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