
Journal for Geometry and Graphics 7 (2003), No. 1, 001021 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 BR_{1}R_{2}C, CR_{3}R_{4}A, AR_{5}R_{6}B be rectangles build on sides of a triangle ABC such that oriented distances BR_{1}, CR_{3}, AR_{5} are λBC, λCA, λAB for some real number λ. We explore the homology and orthology relation of the triangle on central points of triangles AR_{4}R_{5}, BR_{6}R_{1}, CR_{2}R_{3} (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. FullTextpdf (463 KB) for subscribers only. 