Geodesic
Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence
Matematičeskoe obrazovanie, no. 1 (2019), pp. 2-8 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MO_2019_1_a0,
     author = {V. K. Gavrilov},
     title = {Proportional segments, a polygon, and {Chevy's} lines into a circle of the 7-th year students' research competence},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {2--8},
     year = {2019},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2019_1_a0/}
}
TY  - JOUR
AU  - V. K. Gavrilov
TI  - Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence
JO  - Matematičeskoe obrazovanie
PY  - 2019
SP  - 2
EP  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MO_2019_1_a0/
LA  - ru
ID  - MO_2019_1_a0
ER  - 
%0 Journal Article
%A V. K. Gavrilov
%T Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence
%J Matematičeskoe obrazovanie
%D 2019
%P 2-8
%N 1
%U http://geodesic.mathdoc.fr/item/MO_2019_1_a0/
%G ru
%F MO_2019_1_a0
V. K. Gavrilov. Proportional segments, a polygon, and Chevy's lines into a circle of the 7-th year students' research competence. Matematičeskoe obrazovanie, no. 1 (2019), pp. 2-8. http://geodesic.mathdoc.fr/item/MO_2019_1_a0/

[1] Gavrilov V.K., “Ravenstvo Menelaya, puchok pryamykh i mnogougolnik”, Matematicheskoe obrazovanie, 2017, no. 3(83), 2–6

[2] Lopovok L.M., “Vpisannyi shestiugolnik”, Kvant, 1973, no. 1

[3] Zetel S.I., Novaya geometriya treugolnika, Gosudarstvennoe uchebno-pedagogicheskoe izdatelstvo Ministerstva prosvescheniya RSFSR, M., 1962

[4] Oxman V., Stupel M., Sigler A., “Use of Different Representations of Ceva's Theorem for Development of Geometric Properties of a Triangle”, Journal of Mathematical Sciences, 2015, no. 2, 81–87

[5] Sharygin I.F., “Teoremy Chevy i Menelaya”, Kvant, 1976, no. 11

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

[7] Gavrilov V.K., “Ravenstva Menelaya, Chevy i drugie ravenstva”, Informatsionnye tekhnologii v matematike i matematicheskom obrazovanii, Materialy V Vserossiiskoi nauchno-metodicheskoi konferentsii s mezhdunarodnym uchastiem, Krasnoyarsk, 2016, 8–12