Affine Maps and Feuerbach'sTheorem

Abstract

We give an affine proof of Feuerbach's theorem, by constructing an explicit affine map which takes the nine-point circle of any given Euclidean triangle to the incircle and fixes the Feuerbach point. The proof is shown to be valid in any Hilbert plane which satisfies the parallel postulate.

27 pages, 3 figures. This paper was written in 2009. The proof it discsusses has been generalized in the paper "Synthetic Foundations of Cevian Geometry III: The generalized orthocenter" by the author and Igor Minevich