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A Property of a Triangle Inscribed in a Convex Curve

Published online by Cambridge University Press:  20 November 2018

A. Zirakzadeh
A. Zirakzadeh*
Affiliation:
University of Colorado, Boulder, Colorado
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The purpose of this paper is to prove the following theorem:

Theorem. Given a convex curve C, of perimeter length I and three points M, N, and P which divide the perimeter of C into three parts of equal length, the perimeter length of the triangle MNP is never less than ½l. Equality holds only in the case where C is an equilateral triangle and M, N, and P are the mid-points of the three sides.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 777 - 786
Copyright
Copyright © Canadian Mathematical Society 1964