The centres of two circles \( C_{1} \) and \( C_{2} \) each of unit...

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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
\( \mathrm{P} \) 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:
[IIT 2009]
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