Geometry

   

Two Remarkable Ortho-Homological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache

In a previous paper [5] we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously. In this article we call attention to two remarkable ortho-homological triangles (the given triangle ABC and its first Brocard's triangle), and using the Sondat's theorem relative to orthological triangles, we emphasize on four important collinear points in the geometry of the triangle. Orthological / homological / orthohomological triangles in the 2D-space are generalized to orthological / homological / orthohomological polygons in 2D-space, and even more to orthological / homological / orthohomological triangles, polygons, and polyhedrons in 3D-space.

Comments: 11 pages

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Submission history

[v1] 2 Sep 2010
[v2] 4 Sep 2010
[v3] 5 Sep 2010

Unique-IP document downloads: 275 times

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