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IIT JEE Advanced 2009 Paper 2
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© examsnet.com
Question : 51
Total: 57
The centres of two circles
C
1
and
C
2
each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of
C
1
and
C
2
and C bea circle touching circles
C
1
and
C
2
externally. If a common tangent to
C
1
and C passing through P is also a common tangent to
C
2
and C, then the radius of the circle C is _____.
Your Answer:
Validate
Solution:
We have
cos α =
2
√
2
3
sin α =
1
3
tan α =
2
√
2
R
⇒ R =
2
√
2
t
a
n
α
= 8 units.
Alternate Method: We have
(
R
+
1
)
2
=
(
R
−
1
)
2
+
(
4
√
2
)
2
⇒ R = 8
© examsnet.com
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