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The centres of two circles C1 and C2, ea...

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 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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