A 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 1 / 2. What is r ?
Answer Choices
A. 2 \sqrt{2}+2 \sqrt{3}
B. 3 \sqrt{3}+\sqrt{2}
C. 2 \sqrt{6}+\sqrt{3}
D. 3 \sqrt{2}+\sqrt{6}
E. 6 \sqrt{2}-\sqrt{3}