A New Proof of Feuerbach’s Theorem

Ion; Florentin

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

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Volume 2 • Issue 2 • PP: 41-44 • 2023

A New Proof of Feuerbach’s Theorem

Ion Patrascu ^1*

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,

Florentin Smarandache ²

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¹“Frații Buzești” National College, Bld. Stirbei Voda, nr. 5, Craiova, Dolj, Romania

²University of New Mexico, Mathematics, Physics and Natural Sciences Division, 705 Gurley Ave., Gallup, NM 87301, USA

* Corresponding Author.

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

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

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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.

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Patrascu, Ion, Smarandache, Florentin. "A New Proof of Feuerbach’s Theorem." Prospects for Applied Mathematics and Data Analysis, vol. Volume 2, no. Issue 2, 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, Volume 2(Issue 2), 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 Volume 2, no. Issue 2 (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, Volume 2(Issue 2), pp. 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. 2023;Volume 2(Issue 2):41-44. DOI: https://doi.org/10.54216/PAMDA.020205

I. Patrascu, F. Smarandache, "A New Proof of Feuerbach’s Theorem," Prospects for Applied Mathematics and Data Analysis, vol. Volume 2, no. Issue 2, pp. 41-44, 2023. DOI: https://doi.org/10.54216/PAMDA.020205

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