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 $BC$? $\textbf{(A)}\ 11\qquad$ $\textbf{(B)}\ 28\qquad$ $\textbf{(C)}\ 33\qquad$ $\textbf{(D)}\ 61\qquad$ $\textbf{(E)}\ 72$
In $\triangle ABC$, $AB=40$, $AC=47$. A circle with center $A$ and radius $AB$ intersects $\overline{BC}$ at $B,X$, and $\overline{BX},\overline{CX}$ have integer lengths. What is $BC$?
