2008 AMC 12B Problem 21

Two circles of radius 1 are to be constructed as follows. The center of circle A is chosen uniformly and at random from the line segment joining (0,0) and (2,0). The center of circle B is chosen uniformly and at random, and independently of the first choice, from the line segment joining (0,1) to (2,1). What is the probability that circles A and B intersect?

\textbf{(A)} \; \frac {2 + \sqrt {2}}{4} \qquad \textbf{(B)} \; \frac {3\sqrt {3} + 2}{8} \qquad \textbf{(C)} \; \frac {2 \sqrt {2} - 1}{2} \qquad \textbf{(D)} \; \frac {2 + \sqrt {3}}{4} \qquad \textbf{(E)} \; \frac {4 \sqrt {3} - 3}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.