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The centers of two circles C(1) and C(2)...

The centers 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 midpoint of the line segment joining the centres of `C_(1)` and `C_(2)` and C be a 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 tangnet to `C_(2)` and C, then find the radius of circle C.

Text Solution

Verified by Experts

The correct Answer is:
8
`(r+1)^(2) = alpha^(2)+9`

`r^(2)+8=alpha^(2)`
`rArr r^(2) +2r+1= r^(2)+8+9`
`rArr 2r = 16 rArr r= 8`
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