1975 AHSME Problems/Problem 20

Let $BM=CM=x$. Then, by Stewart's Theorem, we have \[2x^3+18x=16x+64x\] \[\implies x^2+9=40\] \[\implies x=\sqrt{31}\implies BC=\boxed{2\sqrt{31}}.\] The answer is $\textbf{(B)}.$ -brainiacmaniac31

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