Radius of first circle $r_1 = 16$ cm, Radius of second circle $r_2 = 9$ cm. The circles touch each other externally.

For two circles touching externally, the length of the direct common tangent is simply $2$ times the geometric mean of the radii: $2\sqrt{r_1 \cdot r_2}$.

Many students confuse the direct common tangent length formula $L = 2\sqrt{r_1 r_2}$ with the transverse common tangent length formula $L = \sqrt{d^2 - (r_1 + r_2)^2}$, where $d$ is the distance between centers.

This concept is a classic in coordinate geometry and trigonometry; specifically, problems involving circles touching externally often appear alongside problems requiring finding the distance between centers, which is simply $r_1 + r_2$.