engleski

HOMOLOGY AND ORTHOLOGY WITH TRIANGLES FROM CENTRAL POINTS OF VARIABLE FLANKS

Here we continue from the paper "Loci related to variable flanks" our 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 lambda|BC|, lambda|CA|, lambda|AB| for some real lambda. 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.

triangle; extriangle; flanks; central points; Kiepert parabola; Kiepert hyperbola; homologic; orthologic; envelope; anticomplementary; complementary; Brocard; orthic; tangential; Euler; Torricelli; Napoleon

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