1994 AHSME Problem 29

Points A, B and C on a circle of radius r are situated so that AB=AC, AB>r, and the length of minor arc BC is r. If angles are measured in radians, then AB/BC= \textbf{(A)}\ \frac{1}{2}\csc{\frac{1}{4}} \qquad\textbf{(B)}\ 2\cos{\frac{1}{2}} \qquad\textbf{(C)}\ 4\sin{\frac{1}{2}} \qquad\textbf{(D)}\ \csc{\frac{1}{2}} \qquad\textbf{(E)}\ 2\sec{\frac{1}{2}}

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