The two circles pictured have the same center C. Chord AD is tangent to the inner circle at B, AC is 10, and chord AD has length 16. What is the area between the two circles?[asy]
unitsize(45);
import graph; size(300); real lsf = 0.5; pen dp = linewidth(0.7) + fontsize(10); defaultpen(dp); pen ds = black; pen xdxdff = rgb(0.49,0.49,1);
draw((2,0.15)--(1.85,0.15)--(1.85,0)--(2,0)--cycle); draw(circle((2,1),2.24)); draw(circle((2,1),1)); draw((0,0)--(4,0)); draw((0,0)--(2,1)); draw((2,1)--(2,0)); draw((2,1)--(4,0));
dot((0,0),ds); label("A", (-0.19,-0.23),NE*lsf); dot((2,0),ds); label("B", (1.97,-0.31),NE*lsf); dot((2,1),ds); label("C", (1.96,1.09),NE*lsf); dot((4,0),ds); label("D", (4.07,-0.24),NE*lsf); clip((-3.1,-7.72)--(-3.1,4.77)--(11.74,4.77)--(11.74,-7.72)--cycle);
[/asy]<spanclass=′latex−bold′>(A)</span> 36π<spanclass=′latex−bold′>(B)</span> 49π<spanclass=′latex−bold′>(C)</span> 64π<spanclass=′latex−bold′>(D)</span> 81π<spanclass=′latex−bold′>(E)</span> 100π geometryinvariantPythagorean Theorem