2014 AMC 10B 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}\qquad\textbf{(B) }\frac{1}{4}\qquad\textbf{(C) }\frac{2-\sqrt{2}}{2}\qquad\textbf{(D) }\frac{1}{3}\qquad\textbf{(E) }\frac{1}{2}\qquad

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