Geodesic
Homology and Orthology with Triangles for Central Points of Variable Flanks
Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 001-022 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51N20
Mots-clés : triangle, extriangle, flanks, central points, Kiepert parabola, Kiepert hyperbola, homologic, orthologic, envelope, anticomplementary, complementary, Brocard, orthic, tangential, Euler, Torricelli, Napoleon 
@article{JGG_2003_7_1_JGG_2003_7_1_a0,
     author = {Z. Cerin},
     title = {Homology and {Orthology} with {Triangles} for {Central} {Points} of {Variable} {Flanks}},
     journal = {Journal for geometry and graphics},
     pages = {001--022},
     year = {2003},
     volume = {7},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a0/}
}
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Z. Cerin. Homology and Orthology with Triangles for Central Points of Variable Flanks. Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 001-022. http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a0/