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Journal for Geometry and Graphics 7 (2003), No. 1, 001--021
Copyright Heldermann Verlag 2003

Homology and Orthology with Triangles for Central Points of Variable Flanks

Zvonko Cerin
Kopernikova 7, HR 10010 Zagreb, Croatia, cerin@math.hrx

Here we continue our previous study of the following geometric configuration. Let BR1R2C, CR3R4A, AR5R6B be rectangles build on sides of a triangle ABC such that oriented distances |BR1|, |CR3|, |AR5| are λ|BC|, λ|CA|, λ|AB| for some real number λ. We explore the homology and orthology relation of the triangle on central points of triangles AR4R5, BR6R1, CR2R3 (like centroids, circumcenters, and orthocenters) and several natural triangles associated to ABC (as its orthic, anticomplementary, and complementary triangle). In some cases we can identify which curves trace their homology and orthology centers and which curves envelope their homology axis.

Keywords: triangle, extriangle, flanks, central points, Kiepert parabola, Kiepert hyperbola, homologic, orthologic, envelope, anticomplementary, complementary, Brocard, orthic, tangential, Euler, Torricelli, Napoleon.

MSC: 51N20.

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