1994 AHSME Problems/Problem 29

Problem

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 $AB/BC=$ $[asy] draw(Circle((0,0), 13)); draw((-13,0)--(12,5)--(12,-5)--cycle); dot((-13,0)); dot((12,5)); dot((12,-5)); label("A", (-13,0), W); label("B", (12,5), NE); label("C", (12,-5), SE); [/asy]$ $\textbf{(A)}\ \frac{1}{2}\csc{\frac{1}{4}} \qquad\textbf{(B)}\ 2\cos{\frac{1}{2}} \qquad\textbf{(C)}\ 4\sin{\frac{1}{2}} \qquad\textbf{(D)}\ \csc{\frac{1}{2}} \qquad\textbf{(E)}\ 2\sec{\frac{1}{2}}$

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1994 AHSME Problems/Problem 29

Problem

Solution