2007/08/10 by Georgi Ganchev, Ganchev, Georgi, Николай Николов +2
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications #Primary: 51M04 #Secondary: 51M16 #math.GM #msc:51M04 #msc:51M16
paper · pdf · doi:10.48550/arxiv.0708.1374
11 pages, 8 figures
arxiv created 2007/08/10 · openalex publication_date 2007/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.