In a internal angle bisectors

MATHEMATICS · Subjective · AoPS · Mathematics · Introduction to Inequalities · x Marks the Spot

Problem

In a

\triangle ABC

internal angle bisectors

AI

,

BI

and

CI

are produced to meet opposite sides in

A'

,

B'

and

C'

, respectively. Prove that the maximum value of

\frac{AI \cdot BI \cdot CI}{AA' \cdot BB' \cdot CC'}

is

\frac{8}{27}

.

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