1996 AHSME Problem 20

In the xy-plane, what is the length of the shortest path from (0,0) to (12,16) that does not go inside the circle (x-6)^{2}+(y-8)^{2}= 25?

\text{(A)}\ 10\sqrt 3\qquad\text{(B)}\ 10\sqrt 5\qquad\text{(C)}\ 10\sqrt 3+\frac{ 5\pi}{3}\qquad\text{(D)}\ 40\frac{\sqrt{3}}{3}\qquad\text{(E)}\ 10+5\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.