AMC 10 2014b Problem 19

Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle? $\textbf{(A)}\ \frac{1}{6} \textbf{(B)}\ \frac{1}{4} \textbf{(C)}\ \frac{2-\sqrt{2}}{2} \textbf{(D)}\ \frac{1}{3} \textbf{(E)}\ \frac{1}{2}$