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1963 AMC 12 Question 22

AMC12 · 1963 AMC 12

Question 22

Acute-angled triangle $ABC$ is inscribed in a circle with center at $O;$ $\overset{\frown}{AB}=120^\circ$ and $\overset{\frown}{BC}=72^\circ.$ A point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC.$ Then the ratio of the magnitudes of angles $OBE$ and $BAC$ is:
  1. $\dfrac5{18}$
  2. $\dfrac29$
  3. $\dfrac14$
  4. $\dfrac13$
  5. $\dfrac49$