1963 AHSME Problem 22

Acute-angled \triangle ABC is inscribed in a circle with center at O; \stackrel \frown {AB} = 120 and \stackrel \frown {BC} = 72. A point E is taken in minor arc AC such that OE is perpendicular to AC. Then the ratio of the magnitudes of \angle OBE and \angle BAC is:

\textbf{(A)}\ \frac{5}{18}\qquad \textbf{(B)}\ \frac{2}{9}\qquad \textbf{(C)}\ \frac{1}{4}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{4}{9}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.