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 $X Y$ is outside the circle?
(A) 29.3
(B) 28.3
(C) 33.3
(D) 25.0
(E) 16.7

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-061.jpg?height=391&width=377&top_left_y=1100&top_left_x=1340)
Since we are looking for the percentage of the whole length, we may take the side length of the square to be any convenient value, as the actual length will not affect the final answer.

Let us assume that the side length of the square is 2 . Then the diameter of the circle is also 2 because the width of the square and the diameter of the circle are equal.

Using the Pythagorean Theorem, $X Y^{2}=2^{2}+2^{2}=4+4=8$ or $X Y=\sqrt{8}$.

The portion of line segment $X Y$ lying outside the circle has length $X Y$ minus the diameter of

the circle, or $\sqrt{8}-2$.
The percentage of line segment $X Y$ lying outside the circle is $\frac{\sqrt{8}-2}{\sqrt{8}} \times 100 \% \approx 29.3 \%$.

ANSWER: (A)