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) to (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?
Answer Choices
A. \dfrac{2+\sqrt{2}}{4}
B. \dfrac{3 \sqrt{3}+2}{8}
C. \dfrac{2 \sqrt{2}-1}{2}
D. \dfrac{2+\sqrt{3}}{4}
E. \dfrac{4 \sqrt{3}-3}{4}