7. The center of a unit square coincides with the center of a circle, and the square is inside the circle. If a point is randomly selected on the circle, the probability that this point can see two complete sides of the square is $\frac{1}{2}$, then the radius of the circle is . $\qquad$
7. $\frac{\sqrt{4+2 \sqrt{2}}}{2}$ Detailed explanation: On the minor arc between the adjacent sides of the square, you can see two complete sides. From the given condition “the probability of seeing two complete sides of the square is $\frac{1}{2}$”, we know that the 8 intersection points of the extensions of the square's sides with the circle divide the circumference into 8 equal parts. Therefore, the radius of the circle is $\frac{\sqrt{4+2 \sqrt{2}}}{2}$.