AMC 8 2008 Problem 18

Two circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, starting at $A$ and ending at $K$. How many meters does the aardvark run?

$\textbf{(A)}\ 10\pi+20 \textbf{(B)}\ 10\pi+30 \textbf{(C)}\ 10\pi+40 \textbf{(D)}\ 20\pi+20 \\ \textbf{(E)}\ 20\pi+40$