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Mathematics
Problem
Three circles are defined by the equations:
S
1
:
x
2
+
y
2
=
1
S_{1}: x^{2} + y^{2} = 1
S
1
:
x
2
+
y
2
=
1
,
S
2
:
x
2
+
y
2
−
2
x
=
0
S_{2}: x^{2} + y^{2} - 2x = 0
S
2
:
x
2
+
y
2
−
2
x
=
0
, and
S
3
:
x
2
+
y
2
−
2
y
=
0
S_{3}: x^{2} + y^{2} - 2y = 0
S
3
:
x
2
+
y
2
−
2
y
=
0
. Find the coordinates of the Radical Center, the unique point having equal power with respect to all three circles.
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