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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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