Problem
1975 AHSME Problem 20
In the adjoining figure \triangle ABC is such that AB = 4 and AC = 8. If M is the midpoint of BC and AM = 3, what is the length of BC?
![[asy] draw((0,0)--(2.8284,2)--(8,0)--cycle); draw((2.8284,2)--(4,0)); label("A",(2.8284,2),N); label("B",(0,0),S); label("C",(8,0),S); label("M",(4,0),S); [/asy]](/static/aops/a1a767bcf7946a7b1bd09cf2e1025ce0d106ed1d.png)
\begin{array}{l} \textbf{(A)}\ 2\sqrt{26} \qquad \textbf{(B)}\ 2\sqrt{31} \qquad \textbf{(C)}\ 9 \qquad \textbf{(D)}\ 4+2\sqrt{13} \qquad\\ \textbf{(E)}\ \text{not enough information given to solve the problem} \end{array}
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