AMC 12 2013a Problem 19

In $\bigtriangleup ABC$, $AB = 86$, and $AC = 97$. A circle with center $A$ and radius $AB$ intersects $\overline{BC}$ at points $B$ and $X$. Moreover $\overline{BX}$ and $\overline{CX}$ have integer lengths. What is $BC$?

\textbf{(A)} \ 11 \textbf{(B)} \ 28 \textbf{(C)} \ 33 \textbf{(D)} \ 61 \textbf{(E)} \ 72