When Euler (circle) meets Poncelet (Porism)
Liliana Gabriela Gheorghe
TL;DR
This paper explores the geometric relationship between triangles sharing the same circumcircle and Euler circle, introducing a poristic circle that enables solving the problem via Poncelet porism.
Contribution
It identifies a new poristic circle that links the circumcircle and Euler circle sharing triangles, expanding the application of Poncelet porism.
Findings
Identifies a poristic circle connecting the given circles.
Provides a method to find all triangles sharing the same circumcircle and Euler circle.
Extends Poncelet porism to a new geometric configuration.
Abstract
We describe all triangles that shares the same circumcircle and Euler circle. Although this two circles do not form a poristic pair of circles, we find a poristic circle "in-between" that enable to solve this problem using Poncelet porism.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Advanced Materials and Mechanics