Three points related to the incenter and excenters of a triangle.
type: Item
instance of: scholarly article
title: Three points related to the incenter and excenters of a triangle.
zbMATH Open document ID: 1151.51301
DOI: 10.4171/EM/35
author: Boris Odehnal
published in: Elemente der Mathematik
publication date: 2008-12-22T00:00:00Z
review text: Summary: The incenter and the three excenters of a triangle \(\triangle\) are the centers of those four circles touching every side of \(\triangle\). From these points three other points can be derived. The resulting triangle \(\triangle_S\) is produced from the triangle \(\triangle_A\) of the excenters by a \(180^\circ\) rotation around the Feuerbach point of \(\triangle\). The triangles \(\triangle_A\) and \(\triangle_S\) share the Euler line and the Feuerbach nine-point circle. The author uses elementary means to prove these and other results connected with them.
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 5480873
MaRDI profile type: Publication
cites work: Q3273607
cites work: Triangle centers as functions
description: scientific article; zbMATH DE number 5480873