{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)} \\; \\frac {2 + \\sqrt {2}}{4} \\qquad \\textbf{(B)} \\; \\frac {3\\sqrt {3} + 2}{8} \\qquad \\textbf{(C)} \\; \\frac {2 \\sqrt {2} - 1}{2} \\qquad \\textbf{(D)} \\; \\frac {2 + \\sqrt {3}}{4} \\qquad \\textbf{(E)} \\; \\frac {4 \\sqrt {3} - 3}{4}$
\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2008 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p22", "prev": "/problem/08_amc12B_p20"}}