The centres of two circles C_1 and C_2 each of unit radius are at a...

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 tangents 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