MathDB

Let

G

be the centroid of a triangle

ABC

and let

d

be a line that intersects

AB

and

AC

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]

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