Geodesic
Two New Analytical and Two New Geometrical Solutions for the Weighted Fermat-Torricelli Problem in the Euclidean Plane
Journal for geometry and graphics, Tome 19 (2015) no. 1, pp. 31-42 Cet article a éte moissonné depuis la source Heldermann Verlag

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We obtain two analytic solutions for the weighted Fermat-Torricelli problem in the Euclidean Plane which states: given three points in the Euclidean plane and a positive real number (weight) which correspond to each point, find the point such that the sum of the weighted distances to these three points is minimized. Furthermore, we give two new geometrical solutions for the the weighted Fermat-Torricelli problem (weighted Fermat-Torricelli point), by using the floating equilibrium condition of the weighted Fermat-Torricelli problem (first geometric solution) and a generalization of Hofmann's rotation proof under the condition of equality of two given weights (second geometric solution).
Classification : 51M04, 51M16, 51M15, 74P20
Mots-clés : Weighted Fermat-Torricelli point, floating case, absorbed case, median, ruler and compass construction 
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     author = {A. N. Zachos },
     title = {Two {New} {Analytical} and {Two} {New} {Geometrical} {Solutions} for the {Weighted} {Fermat-Torricelli} {Problem} in the {Euclidean} {Plane}},
     journal = {Journal for geometry and graphics},
     pages = {31--42},
     year = {2015},
     volume = {19},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2015_19_1_JGG_2015_19_1_a2/}
}
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A. N. Zachos . Two New Analytical and Two New Geometrical Solutions for the Weighted Fermat-Torricelli Problem in the Euclidean Plane. Journal for geometry and graphics, Tome 19 (2015) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/JGG_2015_19_1_JGG_2015_19_1_a2/