Geodesic
From equality of Pythagoras to equality of Ptolemy
Matematičeskoe obrazovanie, no. 1 (2021), pp. 2-4 
V. K. Gavrilov. From equality of Pythagoras to equality of Ptolemy. Matematičeskoe obrazovanie, no. 1 (2021), pp. 2-4. http://geodesic.mathdoc.fr/item/MO_2021_1_a0/
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     title = {From equality of {Pythagoras} to equality of {Ptolemy}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a quadrilateral inscribed in a circle, the connection between Ptolemy's equality and the equality of Pythagoras is noted. A formula is obtained for the ratio of the diagonals of the quadrilateral, the lengthes of the diagonals are determined.

[1] Ya. P. Ponarin, Elementarnaya geometriya, v. 1, MTsNMO, M., 2004

[2] S. A. Anischenko, Lektsii po geometrii, v. 1, Izdatelstvo KGPU, Krasnoyarsk, 1988

[3] , 2012 https://nashaucheba.ru/v7370/referat-Teorema Ptolemeya-fail n1.doc

[4] A. P. Kiselev, Geometriya, ed. N. A. Glagolev, FIZMATLIT, M., 2004

[5] Yu. V. Prokhorov (gl. red.), BES Matematika, “Bolshaya Rossiiskaya entsiklopediya”, M., 1998

[6] V. K. Gavrilov, “Ot ravenstva Pifagora k ravenstvu Ptolemeya”, Informatsionnye tekhnologii v matematike i matematicheskom obrazovanii, Materialy VII Vserossiiskoi nauchno-metodicheskoi konferentsii s mezhdunarodnym uchastiem (Krasnoyarsk, 2018), 87–89