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Problem Description Amy painted a dart board over a square clock face using the "hour positions" as boundaries. [See figure.] If \(t\) is the area of one of the eight triangular regions such as that between \(12\) o'clock and \(1\) o'clock, and \(q\) is the area of one of the four corner quadrilaterals such as that between \(1\) o'clock and \(2\) o'clock, then \(\frac{q}{t}=\) [asy] size((80)); draw((0,0)--(4,0)--(4,4)--(0,4)--(0,0)--(.9,0)--(3.1,4)--(.9,4)--(3.1,0)--(2,0)--(2,4)); draw((0,3.1)--(4,.9)--(4,3.1)--(0,.9)--(0,2)--(4,2)); [/asy] $$ \textbf{(A)}\ 2\sqrt{3}-2 \qquad\textbf{(B)}\ \frac{3}{2} \qquad\textbf{(C)}\ \frac{\sqrt{5}+1}{2} \qquad\textbf{(D)}\ \sqrt{3} \qquad\textbf{(E)}\ 2 $$

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