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Mathematics
Mathematics
Problem
Prove that the length of the common chord of the two circles :
(
x
−
a
)
2
+
(
y
−
b
)
2
=
c
2
(x - a)^2 + (y - b)^2 = c^2
(
x
−
a
)
2
+
(
y
−
b
)
2
=
c
2
and
(
x
−
b
)
2
+
(
y
−
a
)
2
=
c
2
is
4
c
2
−
2
(
a
−
b
)
2
.
\text{and } (x - b)^2 + (y - a)^2 = c^2 \text{ is } \sqrt{4c^2 - 2(a - b)^2}.
and
(
x
−
b
)
2
+
(
y
−
a
)
2
=
c
2
is
4
c
2
−
2
(
a
−
b
)
2
.
Find also the condition when the given circles touch.
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