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

View Item 