MathDB

aAB < AG < b AB and c AB < BG < d AB if G centroid , G and GA > GB > GC

Source: 1979 Swedish Mathematical Competition p6

March 26, 2021

Geometric InequalitiesgeometryCentroid

Problem Statement

Find the sharpest inequalities of the form

a\cdot AB < AG < b\cdot AB

and

c\cdot AB < BG < d\cdot AB

for all triangles

ABC

with centroid

G

such that

GA > GB > GC