AHSME 1970 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 a point $X$ inside the square. How far is $X$ from the side of $CD$? $\text{(A) } \tfrac{1}{2} s(\sqrt{3}+4) \text{(B) } \tfrac{1}{2} s\sqrt{3} \text{(C) } \tfrac{1}{2} s(1+\sqrt{3}) \text{(D) } \tfrac{1}{2} s(\sqrt{3}-1) \text{(E) } \tfrac{1}{2} s(2-\sqrt{3})$