326 200
Full Length Article
Prospects for Applied Mathematics and Data Analysis
Volume 2 , Issue 2, PP: 41-44 , 2023 | Cite this article as | XML | Html |PDF

Title

A New Proof of Feuerbach’s Theorem

  Ion Patrascu 1 * ,   Florentin Smarandache 2

1  “Frații Buzești” National College, Bld. Stirbei Voda, nr. 5, Craiova, Dolj, Romania
    (patrascu_ion@yahoo.com)

2  University of New Mexico, Mathematics, Physics and Natural Sciences Division, 705 Gurley Ave., Gallup, NM 87301, USA
    (smarand@unm.edu)

Full Text Download


Doi   :   https://doi.org/10.54216/PAMDA.020205

Received: April 17, 2023 Accepted: October 25, 2023

Abstract :

Feuerbach’s theorem on the tangent of the circle of the nine points and the inscribed and exinscribed circle is considered one of the most beautiful theorems in geometry. In this paper, we offer a basic proof of this theorem starting from one of Gh. Buicliu’s ideas [1].

Keywords :

Feuerbach’s theorem: circle of the nine points; inscribed circles; exinscribed circles

References :

[1]. Gh. Buicliu: Probleme de construcții geometrice cu rigla și compasul. Tehnica (publishing house), Bucharest, 1967.

[2]. Florentin Smarandache, Ion Patrascu: The Geometry of Homological Triangles. Education Publisher, Colombus, Ohio, 2012.

 

Cite this Article as :
Style #
MLA Ion Patrascu, Florentin Smarandache. "A New Proof of Feuerbach’s Theorem." Prospects for Applied Mathematics and Data Analysis, Vol. 2, No. 2, 2023 ,PP. 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
APA Ion Patrascu, Florentin Smarandache. (2023). A New Proof of Feuerbach’s Theorem. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
Chicago Ion Patrascu, Florentin Smarandache. "A New Proof of Feuerbach’s Theorem." Journal of Prospects for Applied Mathematics and Data Analysis, 2 no. 2 (2023): 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
Harvard Ion Patrascu, Florentin Smarandache. (2023). A New Proof of Feuerbach’s Theorem. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
Vancouver Ion Patrascu, Florentin Smarandache. A New Proof of Feuerbach’s Theorem. Journal of Prospects for Applied Mathematics and Data Analysis, (2023); 2 ( 2 ): 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
IEEE Ion Patrascu, Florentin Smarandache, A New Proof of Feuerbach’s Theorem, Journal of Prospects for Applied Mathematics and Data Analysis, Vol. 2 , No. 2 , (2023) : 41-44 (Doi   :  https://doi.org/10.54216/PAMDA.020205)
↑