Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(1): 275-286

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.275

Copyright © The Korean Mathematical Society.

Area of triangles associated with a curve II

Dong-Soo Kim, Wonyong Kim, Young Ho Kim, and Dae Heui Park

Chonnam National University, Chonnam National University, Kyungpook National University, Chonnam National University

Abstract

It is well known that the area $U$ of the triangle formed by three tangents to a parabola $X$ is half of the area $T$ of the triangle formed by joining their points of contact. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.

Keywords: triangle, area, parabola, strictly convex curve, plane curvature

MSC numbers: 53A04