Geodesic
Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence
Matematičeskoe obrazovanie, Tome 89 (2019) no. 1, pp. 2-8

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It is received an equality analogous to Chevy's equality for a polygon inscribed into a circumference over the ends of the chords with cross point. A new version of proof of Ponsel's theorem is offered for a polygon inscribed into a circumference with an odd or even numbers of sides. It is offered an analog to Menelaus' theorem for a polygon of “star” type inscribed into a circumference.
Keywords: circle
Mots-clés : proportional segments, polygon, contour, Cheva lines. 
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V. K. Gavrilov. Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence. Matematičeskoe obrazovanie, Tome 89 (2019) no. 1, pp. 2-8. http://geodesic.mathdoc.fr/item/MO_2019_89_1_a0/