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arXiv · 1404.2969

Area of triangles associated with a curve II

Dong-Soo Kim·Wonyong Kim·Young Ho Kim·Dae Heui Park
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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.

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Dong-Soo Kim, Wonyong Kim, Young Ho Kim, Dae Heui Park. 2014-04-10. Area of triangles associated with a curve II. https://arxiv.org/abs/1404.2969

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