AMC 12 2005a Problem 16

Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r > s$ is tangent to both axes and to the second and third circles. What is $r/s$?

import graph;
unitsize(3mm);
defaultpen(linewidth(.8pt)+fontsize(10pt));
dotfactor=3;
pair O0=(9,9), O1=(1,1), O2=(3,1), O3=(1,3);
pair P0=O0+9*dir(-45), P3=O3+dir(70);
pair[] ps={O0,O1,O2,O3};
dot(ps);
draw(Circle(O0,9));
draw(Circle(O1,1));
draw(Circle(O2,1));
draw(Circle(O3,1));
draw(O0--P0,linetype("3 3"));
draw(O3--P3,linetype("2 2"));
draw((0,0)--(18,0));
draw((0,0)--(0,18));
label("$r$",midpoint(O0--P0),NE);
label("$s$",(-1.5,4));
draw((-1,4)--midpoint(O3--P3));

$\textbf{(A) } 5 \textbf{(B) } 6 \textbf{(C) } 8 \textbf{(D) } 9 \textbf{(E) } 10$