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International Contests
Cono Sur Olympiad
2017 Cono Sur Olympiad
2
2
Part of
2017 Cono Sur Olympiad
Problems
(1)
Areas inside convex polygon
Source: Cono Sur Olympiad 2017, problem 2
8/17/2017
Let
A
(
X
Y
Z
)
A(XYZ)
A
(
X
Y
Z
)
be the area of the triangle
X
Y
Z
XYZ
X
Y
Z
. A non-regular convex polygon
P
1
P
2
…
P
n
P_1 P_2 \ldots P_n
P
1
P
2
…
P
n
is called guayaco if exists a point
O
O
O
in its interior such that
A
(
P
1
O
P
2
)
=
A
(
P
2
O
P
3
)
=
⋯
=
A
(
P
n
O
P
1
)
.
A(P_1OP_2) = A(P_2OP_3) = \cdots = A(P_nOP_1).
A
(
P
1
O
P
2
)
=
A
(
P
2
O
P
3
)
=
⋯
=
A
(
P
n
O
P
1
)
.
Show that, for every integer
n
≥
3
n \ge 3
n
≥
3
, a guayaco polygon of
n
n
n
sides exists.
geometry
cono sur