Geodesic
Generalizations of Fagnano's Problem
Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 61-69
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We generalize Fagnano’s famous problem of minimal inscribed perimeter by replacing the orthocenter with an arbitrary interior point P. By adding weights associated with P to Fagnano’s inequality, we show that the new, generalized expression reaches minimum for the pedal triangle of P. We then further generalize our main theorem and derive some extensions by relating them to Fermat-Torricelli problem.
Classification : 51M04, 51M16
Mots-clés : Fagnano's inequality, generalized theorem, extremum problem 
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     author = {T. Q. Hung and N. T. T. Duong},
     title = {Generalizations of {Fagnano's} {Problem}},
     journal = {Journal for geometry and graphics},
     pages = {61--69},
     year = {2021},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a5/}
}
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T. Q. Hung; N. T. T. Duong. Generalizations of Fagnano's Problem. Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 61-69. http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a5/