1976 AHSME Problem 3

The sum of the distances from one vertex of a square with sides of length 2 to the midpoints of each of the sides of the square is

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

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