Isogonal Conjugacy and Fermat Problems

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We consider three types of isogonal conjugacy of two points with respect to a given triangle and characterize any of these types by a geometric equality. As an application to the Fermat problem with positive weights, we prove that in the general case the given weights determine uniquely a point X and the solution to the Fermat problem is the point Y, which is isogonally conjugate of type I to the point X. We obtain a similar characterization of the solution to the Fermat problem in the case of mixed weights as well.
11 pages, 8 figures

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General Mathematics, Primary: 51M04; Secondary: 51M16

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http://salesiana.dossiersoluciones.com/handle/123456789/135859

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1374
 http://arxiv.org/abs/0708.1374

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arXiv