1982 USAMO Problems/Problem 3

Problem

If a point $A_1$ is in the interior of an equilateral triangle $ABC$ and point $A_2$ is in the interior of $\triangle{A_1BC}$ , prove that

$I.Q. (A_1BC) > I.Q.(A_2BC)$ ,

where the isoperimetric quotient of a figure $F$ is defined by

$I.Q.(F) = \frac{\text{Area (F)}}{\text{[Perimeter (F)]}^2}$

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1982 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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