Consider all triangles ABC satisfying the following conditions: AB \equal{} AC, D is a point on AC for which BD⊥AC, AD and CD are integers, and BD^2 \equal{} 57. Among all such triangles, the smallest possible value of AC is
<spanclass=′latex−bold′>(A)</span>9<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>11<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>13
[asy]defaultpen(linewidth(.8pt));
dotfactor=4;pair B = (0,0);
pair C = (5,0);
pair A = (2.5,7.5);
pair D = foot(B,A,C);
dot(A);dot(B);dot(C);dot(D);
label("A", A, N);label("B", B, SW);label("C", C, SE);label("D", D, NE);
draw(A--B--C--cycle);draw(B--D);[/asy]