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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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