AMC 12 2006a Problem 19

Circles with centers $(2,4)$ and $(14,9)$ have radii $4$ and $9$, respectively. The equation of a common external tangent to the circles can be written in the form $y=mx+b$ with $m>0$. What is $b$?

size(150);
defaultpen(linewidth(0.7)+fontsize(8));
draw(circle((2,4),4));draw(circle((14,9),9));
draw((0,-2)--(0,20));draw((-6,0)--(25,0));
draw((2,4)--(2,4)+4*expi(pi*4.5/11));
draw((14,9)--(14,9)+9*expi(pi*6/7));
label("4",(2,4)+2*expi(pi*4.5/11),(-1,0));
label("9",(14,9)+4.5*expi(pi*6/7),(1,1));
label("(2,4)",(2,4),(0.5,-1.5));label("(14,9)",(14,9),(1,-1));
draw((-4,120*-4/119+912/119)--(11,120*11/119+912/119));
dot((2,4)^^(14,9));

$\mathrm{(A) \ } \frac{908}{119} \mathrm{(B) \ } \frac{909}{119} \mathrm{(C) \ } \frac{130}{17} \mathrm{(D) \ } \frac{911}{119} \mathrm{(E) \ } \frac{912}{119}$