Distances between centroid and the sides of a triangle
Source:
November 9, 2010
geometryinradiusinequalitiesrearrangement inequalitygeometry proposed
Problem Statement
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.
Determine the points in a triangle that minimize the sum of the distances to the sides.