A Simple Vector Proof of Feuerbach's Theorem
Metric Geometry
2011-07-07 v1
Abstract
The celebrated theorem of Feuerbach states that the nine-point circle of a nonequilateral triangle is tangent to both its incircle and its three excircles. In this note, we give a simple proof of Feuerbach's Theorem using straightforward vector computations. All required preliminaries are proven here for the sake of completeness.
Keywords
Cite
@article{arxiv.1107.1152,
title = {A Simple Vector Proof of Feuerbach's Theorem},
author = {Michael Scheer},
journal= {arXiv preprint arXiv:1107.1152},
year = {2011}
}
Comments
6 pages, 2 figures