Configurations of inscribed equilateral triangles |
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Authors: | Zvonko Čerin |
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Institution: | (1) Kopernikova 7, 10010 Zagreb, Croatia |
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Abstract: | This paper explores equilateral triangles XYZ with vertices on sidelines of a given triangle ABC such that one side of XYZ is parallel to the corresponding side of ABC. There are six such triangles. They have many interesting properties which we investigate using trilinear coordinates. Our
results improve and add to the earlier results of Blas Herrera Gómez about these configurations. We obtain new characterizations
of several central points of the triangles and identify interesting pairs of triangles that are homologic (or perspective)
and orthologic. The recognition of the Darboux cubic of a triangle is also accomplished in these configurations. Triples of
circles intersecting in a point and six points on a conic also appear.
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Keywords: | 51N20 51M04 14A25 14Q05 |
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