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
Abteilung für Geometrie, Universität für Angewandte Kunst, Oskar-Kokoschka-Platz 2, 1010 Wien, Austria
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.
[ Fulltext-pdf (157 KB)] for subscribers only.