The length of the direct common tangent to two circles of radii r₁
and r₂ and d is the distance between their centres is:

Radii of two circles: $$r_1$$​  and $$r_2$$​​

Distance between their centers: d

​$$\bf \text{Length of the direct common tangent} = \sqrt{d^2 - (r_1 - r_2)^2}$$​​