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Source: AHSME 1963 Problem 22

January 10, 2014
ratioAMC

Problem Statement

Acute-angled triangle ABCABC is inscribed in a circle with center at OO; AB⌢=120\stackrel \frown {AB} = 120 and BC⌢=72\stackrel \frown {BC} = 72. A point EE is taken in minor arc ACAC such that OEOE is perpendicular to ACAC. Then the ratio of the magnitudes of angles OBEOBE and BACBAC is:
<spanclass=′latex−bold′>(A)</span> 518<spanclass=′latex−bold′>(B)</span> 29<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 49<span class='latex-bold'>(A)</span>\ \dfrac{5}{18} \qquad <span class='latex-bold'>(B)</span>\ \dfrac{2}{9} \qquad <span class='latex-bold'>(C)</span>\ \dfrac{1}{4} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{1}{3} \qquad <span class='latex-bold'>(E)</span>\ \dfrac{4}{9}
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