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Mathematics
Mathematics
Problem
Prove that the radical axis of two circles is
⊥
\perp
⊥
the line joining their centers. Use the circles
S
1
:
x
2
+
y
2
=
a
2
S_{1}: x^{2} + y^{2} = a^{2}
S
1
:
x
2
+
y
2
=
a
2
and
S
2
:
(
x
−
d
)
2
+
y
2
=
b
2
S_{2}: (x-d)^{2} + y^{2} = b^{2}
S
2
:
(
x
−
d
)
2
+
y
2
=
b
2
to demonstrate this relationship algebraically.
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