Question 22A circle of radius $r$ is concentric with and outside a regular hexagon of side length $2.$ The probability that three entire sides of the hexagon are visible from a randomly chosen point on the circle is $\frac{1}{2}.$ What is $r?$$2\sqrt{2} + 2\sqrt{3}$$3\sqrt{3} + \sqrt{2}$$2\sqrt{6} + \sqrt{3}$$3\sqrt{2} + \sqrt{6}$$6\sqrt{2} - \sqrt{3}$