A circle with radius 1 is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?[asy]
filldraw((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle,mediumgray,black);
filldraw(Circle((0,0),1), mediumgray,black);
filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);[/asy]<spanclass=′latex−bold′>(A)</span>21<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>25