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The centres of two circles C1 and C2 eac...

The centres of two circles C1 and `C2` 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 C1` and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

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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Knowledge Check

  • The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point 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 tangent to C_(2) and C, then the radius of the circle C, is

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    D
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  • The centres of two C_1 and C_2 , each unit of unit radii, 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 . A third circle C is drawn such that it is externally tangent to both the circles C_1 and C_2 at the same points where the lines passing through P are tangent to the circles C_1 and C_2 . The radius of the circle C is

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