A New Proof of Feuerbach’s Theorem

Ion Patrascu; Florentin Smarandache

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

Prospects for Applied Mathematics and Data Analysis

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)

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&rsquo , 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 :

Patrascu, Ion. , Smarandache, Florentin. A New Proof of Feuerbach’s Theorem. Prospects for Applied Mathematics and Data Analysis, vol. , no. , 2023, pp. 41-44. DOI: https://doi.org/10.54216/PAMDA.020205

Patrascu, I. Smarandache, F. (2023). A New Proof of Feuerbach’s Theorem. Prospects for Applied Mathematics and Data Analysis, (), 41-44. DOI: https://doi.org/10.54216/PAMDA.020205

Patrascu, Ion. Smarandache, Florentin. A New Proof of Feuerbach’s Theorem. Prospects for Applied Mathematics and Data Analysis , no. (2023): 41-44. DOI: https://doi.org/10.54216/PAMDA.020205

Patrascu, I. , Smarandache, F. (2023) . A New Proof of Feuerbach’s Theorem. Prospects for Applied Mathematics and Data Analysis , () , 41-44 . DOI: https://doi.org/10.54216/PAMDA.020205

Patrascu I. , Smarandache F. [2023]. A New Proof of Feuerbach’s Theorem. Prospects for Applied Mathematics and Data Analysis. (): 41-44. DOI: https://doi.org/10.54216/PAMDA.020205

Patrascu, I. Smarandache, F. "A New Proof of Feuerbach’s Theorem," Prospects for Applied Mathematics and Data Analysis, vol. , no. , pp. 41-44, 2023. DOI: https://doi.org/10.54216/PAMDA.020205

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