Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/2334 2022 2022 “Frații Buzești” National College, Bld. Stirbei Voda, nr. 5, Craiova, Dolj, Romania Ion Patrascu University of New Mexico, Mathematics, Physics and Natural Sciences Division, 705 Gurley Ave., Gallup, NM 87301, USA Florentin Smarandache 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]. 2023 2023 41 44 10.54216/PAMDA.020205 https://www.americaspg.com/articleinfo/34/show/2334