Research Article

A note on tangential quadrilaterals

Published in: Quaestiones Mathematicae
Volume 48 , issue 2 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 365–375
DOI: 10.2989/16073606.2024.2396026
Author(s): Pradeep Das Rajiv Gandhi Institute of Petroleum Technology, India, Abhishek Juyal Hemvati Nandan Bahuguna Garhwal University, India, Dustin Moody National Institute of Standards & Technology, USA,
Keywords: 51M04, 14H52, 14G05, 11G05, Tangential quadrilateral, rational quadrilateral, elliptic curve,
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Abstract

A tangential quadrilateral is a convex quadrilateral whose sides are simultaneously tangent to a single circle. In this paper, the primary objective is to construct rational tangential quadrilaterals characterized by having rational area, as well as rational side and diagonal lengths. We relate the existence of such tangential quadrilaterals to properties of a certain elliptic curve. Studying the curve, we are able to construct an infinite family of rational tangential quadrilaterals.
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