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 $\mathrm{C}_1$ and $\mathrm{C}_2$ and C be a circle touching circles $\mathrm{C}_1$ and $\mathrm{C}_2$ externally. If a common tangent to $\mathrm{C}_1$ and C passing through P is also a common tangent to $\mathrm{C}_2$ and C , then the radius of the circle C is