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2010 AMC 10B Question 19

AMC10 · 2010 AMC 10B

Question 19

A circle with center $O$ has area $156\pi.$ Triangle $ABC$ is equilateral, $\overline{BC}$ is a chord on the circle, $OA = 4\sqrt{3},$ and point $O$ is outside $\triangle ABC.$ What is the side length of $\triangle ABC?$
  1. $2\sqrt{3}$
  2. $6$
  3. $4\sqrt{3}$
  4. $12$
  5. $18$