Problem
2008 AMC 12B Problem 4
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?
![[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 ("\(C\)", C, NE); label ("\(D\)", D, NW); label ("\(B\)", B, W); label ("\(A\)", A, E); label ("\(O\)", O, S); label ("\(45^\circ\)", (-0.3,0.1), WNW); label ("\(30^\circ\)", (0.5,0.1), ENE); draw (A--B); draw (O--D); draw (O--C); [/asy]](/static/aops/6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png)
\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}
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