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.
Dong-Soo Kim, Wonyong Kim, Young Ho Kim, and Dae Heui Park
Chonnam National University, Chonnam National University, Kyungpook National University, Chonnam National University
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
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