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Inequality
USAMO
2015
Problem - 2206
Let
A
=
(
2
,
0
)
,
B
=
(
0
,
2
)
,
C
=
(
−
2
,
0
)
, and
D
=
(
0
,
−
2
)
. Compute the greatest possible value of the product
P
A
⋅
P
B
⋅
P
C
⋅
P
D
, where
P
is a point on the circle
x
2
+
y
2
=
9
.
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