Journal for Geometry and Graphics 18 (2014), No. 1, 061--071
Copyright Heldermann Verlag 2014
A Triad of Circles Externally Tangent to the Nine-Point Circle and Internally Tangent to Two Sides of a Triangle
Boris Odehnal
Abteilung für Geometrie, Universität für Angewandte Kunst, Oskar-Kokoschka-Platz 2, 1010 Wien, Austria
boris@geometrie.tuwien.ac.at
We determine the three circles in the interior of an acute triangle Δ which touch the nine-point circle n from the outside and two sides of Δ from the inside. Some perspective triangles related to Δ and the three circles are found. A more general result on tangent triangles related to Apollonian configurations of circles leads to a specific result in the case of a special Apollonian configuration derived from the three circles in question. All constructions are linear once the excircles of the base triangle are constructed.
Keywords: Triangle, nine-point circle, Apollonian problem, tangent triangle, perspective triangles.
MSC: 51N20
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