A property of the centroid of a triangle
Rane, Ujjawal (2021) A property of the centroid of a triangle. At Right Angles (10). pp. 6061. ISSN 25821873
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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: 


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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