{"status": "success", "data": {"description_md": "Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?\n\n$\\text{(A) } \\dfrac{1+\\sqrt2}4 \\quad \\text{(B) } \\dfrac{\\sqrt5-1}2 \\quad \\text{(C) } \\dfrac{\\sqrt3+1}4 \\quad \\text{(D) } \\dfrac{2\\sqrt3}5 \\quad \\text{(E) } \\dfrac{\\sqrt5}3$\n\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/a/a/3/aa3449d7a1f5549a72c1e5be22ee89bd4499ee51.png\" width=\"252\"/>\n</center>", "description_html": "<p>Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?</p>\n<p> <span class=\"katex--inline\">\\text{(A) } \\dfrac{1+\\sqrt2}4 \\quad \\text{(B) } \\dfrac{\\sqrt5-1}2 \\quad \\text{(C) } \\dfrac{\\sqrt3+1}4 \\quad \\text{(D) } \\dfrac{2\\sqrt3}5 \\quad \\text{(E) } \\dfrac{\\sqrt5}3</span> </p>\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/a/a/3/aa3449d7a1f5549a72c1e5be22ee89bd4499ee51.png\" width=\"252\"/>\n</center>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2014 AMC 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10B_p23", "prev": "/problem/14_amc10B_p21"}}