Area of triangles associated with a curve
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 901-909
https://doi.org/10.4134/BKMS.2014.51.3.901
Published online May 31, 2014
Dong-Soo Kim and Kyu-Chul Shim
Chonnam 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 study some properties of $U$ and $T$ for strictly convex plane curves. As a result, we establish a characterization for parabolas.
Keywords : triangle, area, parabola, strictly convex curve, plane curvature
MSC numbers : 53A04
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd