{"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><br>\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 <span class=\"katex--inline\">3, 2</span>, and <span class=\"katex--inline\">1</span>. 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>&#10;<center>&#10;<img class=\"problem-image\" height=\"142\" src=\"https://latex.artofproblemsolving.com/f/e/9/fe9afaa1f9ed8ef23f107f3e17a274aa0a17aeb3.png\" width=\"142\"/>&#10;</center><br/>&#10;<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>&#10;", "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"}}