2013 AMC 12A 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 \qquad \textbf{(B)} \ 28 \qquad \textbf{(C)} \ 33 \qquad \textbf{(D)} \ 61 \qquad \textbf{(E)} \ 72

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.