MathDB
Distances between centroid and the sides of a triangle

Source:

November 9, 2010
geometryinradiusinequalitiesrearrangement inequalitygeometry proposed

Problem Statement

(a)(a) Prove that in a triangle the sum of the distances from the centroid to the sides is not less than three times the inradius, and find the cases of equality. (b)(b) Determine the points in a triangle that minimize the sum of the distances to the sides.