{"status": "success", "data": {"description_md": "Two distinct lines pass through the center of three concentric circles of radii 3, 2, and 1. The area of the shaded region in the diagram is $\\frac{8}{13}$ of the area of the unshaded region. What is the radian measure of the acute angle formed by the two lines? (Note: $\\pi$ radians is $180$ degrees.)\n\n<center>\n<img class=\"problem-image\" height=\"142\" src=\"https://latex.artofproblemsolving.com/f/e/9/fe9afaa1f9ed8ef23f107f3e17a274aa0a17aeb3.png\" width=\"142\"/>\n</center>\n\n$\\mathrm{(A) \\ } \\frac{\\pi}{8} \\qquad \\mathrm{(B) \\ } \\frac{\\pi}{7} \\qquad \\mathrm{(C) \\ } \\frac{\\pi}{6} \\qquad \\mathrm{(D) \\ } \\frac{\\pi}{5} \\qquad \\mathrm{(E) \\ } \\frac{\\pi}{4}$", "description_html": "<p>Two distinct lines pass through the center of three concentric circles of radii 3, 2, and 1. The area of the shaded region in the diagram is  <span class=\"katex--inline\">\\frac{8}{13}</span>  of the area of the unshaded region. What is the radian measure of the acute angle formed by the two lines? (Note:  <span class=\"katex--inline\">\\pi</span>  radians is  <span class=\"katex--inline\">180</span>  degrees.)</p>\n<center>\n<img class=\"problem-image\" height=\"142\" src=\"https://latex.artofproblemsolving.com/f/e/9/fe9afaa1f9ed8ef23f107f3e17a274aa0a17aeb3.png\" width=\"142\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{\\pi}{8} \\qquad \\mathrm{(B) \\ } \\frac{\\pi}{7} \\qquad \\mathrm{(C) \\ } \\frac{\\pi}{6} \\qquad \\mathrm{(D) \\ } \\frac{\\pi}{5} \\qquad \\mathrm{(E) \\ } \\frac{\\pi}{4}</span> </p>\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": "2004 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p22", "prev": "/problem/04_amc10A_p20"}}