Geodesic
Area of a triangle and angle bisectors
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 732-737

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Consider a triangle $ABC$ with given lengths $l_a,l_b,l_c$ of its internal angle bisectors. We prove that in general, it is impossible to construct a square of the same area as $ABC$ using a ruler and compass. Moreover, it is impossible to express the area of $ABC$ in radicals of $l_a,l_b,l_c$.
Keywords: area of a triangle, angle bisectors, solution in radicals.
Mots-clés : ruler and compass construction, Galois group of a polynomial, algebraic equation 
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     author = {A. A. Buturlakin and S. S. Presnyakov and D. O. Revin and S. A. Savin},
     title = {Area of a triangle and angle bisectors},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {732--737},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a53/}
}
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A. A. Buturlakin; S. S. Presnyakov; D. O. Revin; S. A. Savin. Area of a triangle and angle bisectors. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 732-737. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a53/