2009 Gauss 8 Problem 23

In the diagram, the circle is *inscribed* in the square. This means that the circle and the square share points S, T, U, and V, and the width of the square is exactly equal to the diameter of the circle. Rounded to the nearest tenth, what percentage of line segment XY is outside the circle?

\textbf{(A)}\ 29.3\quad \textbf{(B)}\ 28.3\quad \textbf{(C)}\ 33.3\quad \textbf{(D)}\ 25.0\quad \textbf{(E)}\ 16.7

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.