2013 AMC 10A Problem 23

In \triangle 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.