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Nice geometric inequality

Source: Iberoamerican Olympiad 1992, Problem 6

May 14, 2007

inequalitiesgeometrytrigonometrycircumcircleinequalities proposed

Problem Statement

In a triangle

ABC

, points

A_{1}

and

A_{2}

are chosen in the prolongations beyond

A

of segments

B_{1}

and

AC

, such that

AA_{1}=AA_{2}=BC

. Define analogously points

B_{1}

,

B_{2}

,

C_{1}

,

C_{2}

. If

[ABC]

denotes the area of triangle

ABC

, show that

[A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}] \geq 13 [ABC]

.

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