4. In the region
$$
\left\{\begin{array}{l}
\frac{x^{2}}{9}+y^{2} \leqslant 1 \\
x \geqslant 0
\end{array}\right.
$$

the maximum radius of the circle that can be contained is $\qquad$ .
4. $\frac{2 \sqrt{2}}{3}$