Michael J. G. Scheer, A simple vector proof of Feuerbach’s theorem,
Forum Geometricorum, 11 (2011) 205--210.
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.
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