A property of the centroid of a triangle

Rane, Ujjawal (2021) A property of the centroid of a triangle. At Right Angles (10). pp. 60-61. ISSN 2582-1873

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Abstract

In this note, we establish an unexpected property of the centroid of a triangle. Given any triangle ABC, let P be an arbitrary point lying within the triangle. Drop perpendiculars PD, PE, PF to the sides BC, CA, AB respectively. We ask: For which point P does the product PD · PE · PF take its largest possible value? We shall show that for any triangle, PD · PE · PF takes its maximum value when P lies at the centroid of the triangle.

Item Type:	Articles in APF Magazines
Authors:	Rane, Ujjawal
Document Language:	Language English
Uncontrolled Keywords:	Centroid, Perpendicular, Product, Similar Triangles, Quadratic, Maximum
Subjects:	Natural Sciences > Mathematics
Divisions:	Azim Premji University - Bengaluru > University Publications > At Right Angles
Full Text Status:	Public
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/2795
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