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Source:
November 9, 2012
geometry
Problem Statement
How many ordered pairs of real numbers
(
x
,
y
)
(x, y)
(
x
,
y
)
are there such that
x
2
+
y
2
=
200
x^2+y^2 = 200
x
2
+
y
2
=
200
and
(
x
−
5
)
2
+
(
y
−
5
)
2
+
(
x
+
5
)
2
+
(
y
+
5
)
2
\sqrt{(x-5)^2+(y-5)^2}+\sqrt{(x+5)^2+(y+5)^2}
(
x
−
5
)
2
+
(
y
−
5
)
2
+
(
x
+
5
)
2
+
(
y
+
5
)
2
is an integer?
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