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11
Math Prize 2015 Problem 11
Math Prize 2015 Problem 11
Source:
September 22, 2015
Problem Statement
Let
A
=
(
2
,
0
)
A = (2, 0)
A
=
(
2
,
0
)
,
B
=
(
0
,
2
)
B = (0, 2)
B
=
(
0
,
2
)
,
C
=
(
−
2
,
0
)
C = (-2, 0)
C
=
(
−
2
,
0
)
, and
D
=
(
0
,
−
2
)
D = (0, -2)
D
=
(
0
,
−
2
)
. Compute the greatest possible value of the product
P
A
⋅
P
B
⋅
P
C
⋅
P
D
PA \cdot PB \cdot PC \cdot PD
P
A
⋅
PB
⋅
PC
⋅
P
D
, where
P
P
P
is a point on the circle
x
2
+
y
2
=
9
x^2 + y^2 = 9
x
2
+
y
2
=
9
.
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