2012 AMC 10B Problem 21

Four distinct points are arranged on a plane so that the segments connecting them have lengths a, a, a, a, 2a, and b. What is the ratio of b to a?

\textbf{(A)}\ \sqrt{3}\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ \sqrt{5}\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ \pi

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