AHSME 1999 Problem 19

Consider all triangles $ABC$ satisfying in the following conditions: $AB = AC$, $D$ is a point on $\overline{AC}$ for which $\overline{BD} \perp \overline{AC}$, $AC$ and $CD$ are integers, and $BD^{2} = 57$. Among all such triangles, the smallest possible value of $AC$ is

$\textrm{(A)} \ 9 \textrm{(B)} \ 10 \textrm{(C)} \ 11 \textrm{(D)} \ 12 \textrm{(E)} \ 13$