{"status": "success", "data": {"description_md": "On circle $O$, points $C$ and $D$ are on the same side of diameter $\\overline{AB}$, $\\angle AOC = 30^\\circ$, and $\\angle DOB = 45^\\circ$. What is the ratio of the area of the smaller sector $COD$ to the area of the circle? <br><center><img class=\"problem-image\" alt=\"[asy] unitsize(6mm); defaultpen(linewidth(0.7)+fontsize(8pt));  pair C = 3*dir (30); pair D = 3*dir (135); pair A = 3*dir (0); pair B = 3*dir(180); pair O = (0,0); draw (Circle ((0, 0), 3)); label (&quot;\\(C\\)&quot;, C, NE); label (&quot;\\(D\\)&quot;, D, NW); label (&quot;\\(B\\)&quot;, B, W); label (&quot;\\(A\\)&quot;, A, E); label (&quot;\\(O\\)&quot;, O, S); label (&quot;\\(45^\\circ\\)&quot;, (-0.3,0.1), WNW); label (&quot;\\(30^\\circ\\)&quot;, (0.5,0.1), ENE); draw (A--B); draw (O--D); draw (O--C); [/asy]\" class=\"latexcenter\" height=\"172\" src=\"https://latex.artofproblemsolving.com/6/e/f/6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png\" width=\"205\"/></center>\n\n$\\textbf{(A)}\\ \\frac {2}{9} \\qquad \\textbf{(B)}\\ \\frac {1}{4} \\qquad \\textbf{(C)}\\ \\frac {5}{18} \\qquad \\textbf{(D)}\\ \\frac {7}{24} \\qquad \\textbf{(E)}\\ \\frac {3}{10}$\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": "<p>On circle  <span class=\"katex--inline\">O</span> , points  <span class=\"katex--inline\">C</span>  and  <span class=\"katex--inline\">D</span>  are on the same side of diameter  <span class=\"katex--inline\">\\overline{AB}</span> ,  <span class=\"katex--inline\">\\angle AOC = 30^\\circ</span> , and  <span class=\"katex--inline\">\\angle DOB = 45^\\circ</span> . What is the ratio of the area of the smaller sector  <span class=\"katex--inline\">COD</span>  to the area of the circle? <br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(6mm); defaultpen(linewidth(0.7)+fontsize(8pt));  pair C = 3*dir (30); pair D = 3*dir (135); pair A = 3*dir (0); pair B = 3*dir(180); pair O = (0,0); draw (Circle ((0, 0), 3)); label (&#34;\\(C\\)&#34;, C, NE); label (&#34;\\(D\\)&#34;, D, NW); label (&#34;\\(B\\)&#34;, B, W); label (&#34;\\(A\\)&#34;, A, E); label (&#34;\\(O\\)&#34;, O, S); label (&#34;\\(45^\\circ\\)&#34;, (-0.3,0.1), WNW); label (&#34;\\(30^\\circ\\)&#34;, (0.5,0.1), ENE); draw (A--B); draw (O--D); draw (O--C); [/asy]\" height=\"172\" src=\"https://latex.artofproblemsolving.com/6/e/f/6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png\" width=\"205\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {2}{9} \\qquad \\textbf{(B)}\\ \\frac {1}{4} \\qquad \\textbf{(C)}\\ \\frac {5}{18} \\qquad \\textbf{(D)}\\ \\frac {7}{24} \\qquad \\textbf{(E)}\\ \\frac {3}{10}</span> </p>&#10;<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": 2, "problem_name": "2008 AMC 12B Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p05", "prev": "/problem/08_amc12B_p03"}}