The length of the direct common tangent to two circles of radii r1 and r2 and d is the distance between their centres is:
1
\(\rm \sqrt{d^2\left(r_1r_2\right)}\,\)
2
\(\rm \sqrt{d^2-\left(r_1+r_2\right)^2}\,\,\)
3
\(\rm \sqrt{d^2-\left(r_1^2+r_2^2\right)}\,\,\)
4
\(\rm \sqrt{d^2-\left(r_1-r_2\right)^2}\,\,\)