4. Given that $\odot O_{1}$ and $\odot O_{2}$ are externally tangent, their radii are $112$ and $63$, respectively. The segment $A B$ is intercepted by their two external common tangents on their internal common tangent. Then, the length of $A B$ is $\qquad$ .
4.168.

From the tangent theorem, we easily know that
$$
\begin{array}{l}
A B=\text { length of the external common tangent }=\sqrt{(112+63)^{2}-(112-63)^{2}} \\
=2 \sqrt{112 \times 63}=168 .
\end{array}
$$