1970 AHSME Problem 7

Inside square ABCD with side s, quarter-circle arcs with radii s and centers at A and B are drawn. These arcs intersect at point X inside the square. How far is X from side CD?

\begin{array}{l} \textbf{(A) }\frac{1}{2}s(\sqrt{3}+4)\qquad \textbf{(B) }\frac{1}{2}s\sqrt{3}\qquad \textbf{(C) }\frac{1}{2}s(1+\sqrt{3})\qquad\\ \textbf{(D) }\frac{1}{2}s(\sqrt{3}-1)\qquad \textbf{(E) }\frac{1}{2}s(2-\sqrt{3}) \end{array}

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