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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 tangents to C1 and C passing through P is also a common targent to C2 and C1 then the radius of the circle C is ____.

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The radius of the circle C is 8.

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