{"status": "success", "data": {"description_md": "Points $A$ and $B$ lie on a circle centered at $O$, and $\\angle AOB = 60^\\circ$. A second circle is internally tangent to the first and tangent to both $\\overline{OA}$ and $\\overline{OB}$. What is the ratio of the area of the smaller circle to that of the larger circle?\n\n$\\mathrm{(A)}\\ \\frac{1}{16}\\qquad\\mathrm{(B)}\\ \\frac{1}{9}\\qquad\\mathrm{(C)}\\ \\frac{1}{8}\\qquad\\mathrm{(D)}\\ \\frac{1}{6}\\qquad\\mathrm{(E)}\\ \\frac{1}{4}$", "description_html": "<p>Points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  lie on a circle centered at  <span class=\"katex--inline\">O</span> , and  <span class=\"katex--inline\">\\angle AOB = 60^\\circ</span> . A second circle is internally tangent to the first and tangent to both  <span class=\"katex--inline\">\\overline{OA}</span>  and  <span class=\"katex--inline\">\\overline{OB}</span> . What is the ratio of the area of the smaller circle to that of the larger circle?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1}{16}\\qquad\\mathrm{(B)}\\ \\frac{1}{9}\\qquad\\mathrm{(C)}\\ \\frac{1}{8}\\qquad\\mathrm{(D)}\\ \\frac{1}{6}\\qquad\\mathrm{(E)}\\ \\frac{1}{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": 3, "problem_name": "2008 AMC 10A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p17", "prev": "/problem/08_amc10A_p15"}}