2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135859We 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 figuresGeneral MathematicsPrimary: 51M04; Secondary: 51M16text