Benedetto Scimemi, Simple relations regarding the Steiner inellipse
of a triangle,
Forum Geometricorum, 10 (2010) 55--77.
Abstract: By applying analytic geometry within a special Cartesian reference,
based on the Kiepert hyperbola, we prove a great number of relations (collinearities,
similarities, inversions etc.) regarding central points, central lines
and central conics of a triangle. Most - not all - of these statements
are well-known, but somehow dispersed throughout the literature. Some relations
turn out to be easy consequences of the action of a conjugation - an involutory
M"obius transformation - whose fixed points are the foci of the Steiner inellipse.