Journal for Geometry and Graphics 15 (2011), No. 1, 045--067
Copyright Heldermann Verlag 2011
Poristic Loci of Triangle Centers
Boris Odehnal
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1230 Vienna, Austria
boris@geometrie.tuwien.ac.at
The one-parameter family of triangles with common incircle and circumcircle is called a porisitic system of triangles. The triangles of a poristic system can be rotated freely about the common incircle. However this motion is not a rigid body motion for the sidelengths of the triangle are changing. Surprisingly many triangle centers associated with the triangles of the poristic family trace circles while the triangle traverses the poristic family. Other points move on conic sections, some points trace more complicated curves. We shall describe the orbits of centers and some other points. Thereby we are able to answer open questions and verify some older results.
Keywords: Poristic triangles, incircle, excircle, non-rigid body motion, poristic locus, triangle center, circle, conic section.
MSC: 51M04; 51N35
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