Problem 140

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Problem 140: (2010 AMC 10B, 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 $\triangle ABC$? $\textbf{(A)}\ 2\sqrt{3} \qquad$ $ \textbf{(B)}\ 6 \qquad$ $ \textbf{(C)}\ 4\sqrt{3} \qquad$ $ \textbf{(D)}\ 12 \qquad$ $ \textbf{(E)}\ 18$

Solution

Exercise 140: Solution

A circle with center $O$ has area $49\pi$. Triangle $ABC$ is equilateral, $\overline{BC}$ is a chord on the circle, $OA=5\sqrt3$, and point $O$ is outside $\triangle ABC$. What is the side length of $\triangle ABC$?

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