AHSME 1996 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 $(x-6)^{2}+(y-8)^{2}= 25$? $\text{(A)}\ 10\sqrt 3 \text{(B)}\ 10\sqrt 5 \text{(C)}\ 10\sqrt 3+\frac{ 5\pi}{3} \text{(D)}\ 40\frac{\sqrt{3}}{3} \text{(E)}\ 10+5\pi$