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 Pis also a common tangent to $$C_2$$ and C, then the radius ofthe circle C is