Geodesic
Triangles with specified values of the incircle and circumcircle radii
Matematičeskoe obrazovanie, no. 2 (2021), pp. 28-33 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The analysis of triangles given by the radii of the inscribed and circumscribed circles presented in this article can be considered as an example of the successful application of a specially developed universal method for determining a triangle by its elements. 
@article{MO_2021_2_a3,
     author = {S. F. Osinkin},
     title = {Triangles with specified values of the incircle and circumcircle radii},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {28--33},
     year = {2021},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2021_2_a3/}
}
TY  - JOUR
AU  - S. F. Osinkin
TI  - Triangles with specified values of the incircle and circumcircle radii
JO  - Matematičeskoe obrazovanie
PY  - 2021
SP  - 28
EP  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MO_2021_2_a3/
LA  - ru
ID  - MO_2021_2_a3
ER  - 
%0 Journal Article
%A S. F. Osinkin
%T Triangles with specified values of the incircle and circumcircle radii
%J Matematičeskoe obrazovanie
%D 2021
%P 28-33
%N 2
%U http://geodesic.mathdoc.fr/item/MO_2021_2_a3/
%G ru
%F MO_2021_2_a3
S. F. Osinkin. Triangles with specified values of the incircle and circumcircle radii. Matematičeskoe obrazovanie, no. 2 (2021), pp. 28-33. http://geodesic.mathdoc.fr/item/MO_2021_2_a3/

[1] P. Mironescu, L. Panaitopol, “The existence of a triangle with prescribed angle bisector lengths”, Amer. Math. Monthly, 101 (1994), 58–60 | DOI | Zbl

[2] A. Zhukov, I. Akulich, Odnoznachno li opredelyaetsya treugolnik?, Kvant, 2003, no. 1, 29–31

[3] S. Osinkin, “On the existence of a triangle with prescribed bisector lengths”, Forum Geometricorum, 16 (2016), 399–405 | Zbl

[4] S. Osinkin, The method and examples of solving problems analogous to the “problem of three bisectors”, arXiv: 1910.01855v1 [math.H0]

[5] D. O. Shklyarskii, N. N. Chentsov, I. M. Yaglom, Izbrannye zadachi i teoremy elementarnoi matematiki, v. 2, Geometriya (planimetriya), Gos. izd. tekhniko-teoreticheskoi literatury, M., 1952

[6] R. Kurant, G. Robbins, Chto takoe matematika?, MTsNMO, M., 2004

[7] V. I. Golubev, L. N. Erganzhieva, K. K. Mosevich, Postroenie treugolnika, 4-e izd., Laboratoriya znanii, M., 2015