Side Length of the Extension of Napoleon’s
Outer Theorem on Triangle

Silvia Riani; Mashadi; Leli Deswita

doi:https://doi.org/10.14445/22315373/IJMTT-V67I1P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P505

Side Length of the Extension of Napoleon’s Outer Theorem on Triangle

Silvia Riani, Mashadi, Leli Deswita

Abstract

This paper discusses the side lengths of the development of Napoleon's outer theorem on triangles by applying the special case Miquel's theorem. If in Napoleon's theorem the outer triangle uses an equilateral triangle, in this paper it has been modified by using isosceles right triangles as the outer triangle. The new triangle formed has a shape similar to the original triangle. Furthermore, determination of the side length of the new triangle formed utilizes the Pythagorean formula and cosine rule.

Keywords

Miquel point, Napoleon’s theorem, outer Napoleon

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Citation :

Silvia Riani, Mashadi, Leli Deswita, "Side Length of the Extension of Napoleon’s Outer Theorem on Triangle," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 1, pp. 29-35, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P505