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Brazil Contests
Brazil National Olympiad
1992 Brazil National Olympiad
3
The greates-area polygon
The greates-area polygon
Source: Problem 3, Brazil MO 1992
March 18, 2006
geometry
geometry proposed
Problem Statement
Given positive real numbers
x
1
,
x
2
,
…
,
x
n
x_1, x_2, \ldots , x_n
x
1
,
x
2
,
…
,
x
n
find the polygon
A
0
A
1
…
A
n
A_0A_1\ldots A_n
A
0
A
1
…
A
n
with
A
i
A
i
+
1
=
x
i
+
1
A_iA_{i+1} = x_{i+1}
A
i
A
i
+
1
=
x
i
+
1
and which has greatest area.
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