Can you do it without the co-ordinates?

Three circles are tangent to each other:

• the first has center $(0,0)$ and radius 4,

• the second has center $(3,0)$ and radius 1, and

• the third circle has center $(-1,0)$ and radius 3.

Find the radius of a fourth circle tangent to each of these 3 circles to 3 decimal places.