1998 Fermat Problem 24

At some time between 9:30 and 10 o'clock the triangle determined by the minute hand and the hour hand is an isosceles triangle (see diagram). If the two equal angles in this triangle are each twice as large as the third angle, what is the time?

\textbf{(A)}\ 9:35\quad \textbf{(B)}\ 9:36\quad \textbf{(C)}\ 9:37\quad \textbf{(D)}\ 9:38\quad \textbf{(E)}\ 9:39

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