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