A New Proof of Feuerbach’s Theorem

 Ion Patrascu¹, Florentin Smarandache²

¹“Frații Buzești” National College, Bld. Stirbei Voda, nr. 5, Craiova, Dolj, Romania

²University of New Mexico, Mathematics, Physics and Natural Sciences Division,

705 Gurley Ave., Gallup, NM 87301, USA

Email: patrascu_ion@yahoo.com; smarand@unm.edu

Abstract

Feuerbach’s theorem on the tangent of the circle of the nine points and the inscribed and exinscribed circle is considered one of the most beautiful theorems in geometry. In this paper, we offer a basic proof of this theorem starting from one of Gh. Buicliu’s ideas [1].

Keywords: Feuerbach’s theorem: circle of the nine points; inscribed circles; exinscribed circles