English

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

R2 v1 2026-06-21T18:32:58.656Z