The distance between the centres of two circles of radii $1\text{ cm}$ and $7\text{ cm}$ is $10\text{ cm}$. The length of direct tangent (in $\text{cm}$) is

The formula for computing the length of a direct common tangent ($L$) between two circles is:
$$L=\sqrt{d^2-(R-r{)}^2}$$

Where:

* $d=10\text{ cm}$ (distance between the centers)
* $R=7\text{ cm}$ (radius of the larger circle)
* $r=1\text{ cm}$ (radius of the smaller circle)

Substituting the parameters into the formula:

$$L=\sqrt{10^2-(7-1{)}^2}=\sqrt{100-6^2}=\sqrt{100-36}=\sqrt{64}=8\text{ cm}$$