MathDB

geometrical inequality involving the centroid

Source: bmo 1989

April 23, 2007

inequalitiesgeometry proposedgeometry

Problem Statement

Let

G

be the centroid of a triangle

ABC

and let

A

be a line that intersects

G

and

AC

at

B_{1}

and

C_{1}

, respectively, such that the points

A

and

G

are not separated by

d

. Prove that:

[BB_{1}GC_{1}]+[CC_{1}GB_{1}] \geq \frac{4}{9}[ABC]

.

Back to Problems View on AoPS