Geodesic
Inscribed polygons and Heron polynomials
Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 311-331 
V. V. Varfolomeev. Inscribed polygons and Heron polynomials. Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 311-331. http://geodesic.mathdoc.fr/item/SM_2003_194_3_a0/
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     title = {Inscribed polygons and {Heron} polynomials},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Heron's well-known formula expressing the area of a triangle in terms of the lengths of its sides is generalized in the following sense to polygons inscribed in a circle: it is proved that the area is an algebraic function of the lengths of the edges of the polygon. Similar results are proved for the diagonals and the radius of the circumscribed circle. The resulting algebraic equations are studied and elementary geometric applications of the algebraic results obtained are presented.

[1] Sabitov I. Kh., “Obobschennaya formula Gerona–Tartalya i nekotorye ee sledstviya”, Matem. sb., 189:10 (1998), 105–134 | MR | Zbl