This is a multiple-choice question with one or more possible correct answers, so let's examine each statement in turn to select the correct answers.
(A) The circumference of the circle $\(=4 \pi\)$

Since the circumference $=$ diameter $\times \pi$, this means that the diameter of the circle is 4 . That diameter is also the length of a side of the circumscribed square, whose area would then be 16 .
(B) The ratio of the area of the square to the area of the circle $\(=\frac{4}{\pi}\)$.
Let $r$ be the radius of the circle. In this case, the area of the square will be $\(4 r^2\)$ and the area of the circle $\(\pi r^2\)$.

The ratio of the area of the square to the area of the circle will be $\(\frac{4 r^2}{\pi r^2}=\frac{4}{\pi}\)$. This statement will always be true for any circle inscribed in a square, so it doesn't tell us any useful information about this particular square.
(C) The area of the shaded section in the lower left, inside the square but outside the circle, is $4-\pi$.

This looks promising. The area of the shaded area is $\(\frac{1}{4}\)$ the area of the square minus $\(\frac{1}{4}\)$ the area of the circle.

If $r$ is the radius of the circle, then $\(\frac{1}{4}\)$ the area of the square is just $\(r^2\)$, and $\(\frac{1}{4}\)$ the area of the circle is $\(\frac{\pi r^2}{4}\)$.
We can set up our equation using this new statement:

$$
\(r^2-\frac{\pi r^2}{4}=4-\pi\)
$$


Multiply each side by 4 to get:

$$
\(4 r^2-\pi r^2=4(4-\pi)\)
$$


Factor the left side $\(\Rightarrow r^2(4-\pi)=4(4-\pi)\)$
Divide out the $\(4-\pi\)$ from both sides $\(\Rightarrow r^2=4\)$
Square root both sides $\(\Rightarrow r=2\)$.

The length of a side of the square $\(=2 r=4\)$, and the area of the square is 16 .
Answer choices ( $A$ ) and ( $C$ ) are each individually sufficient to answer the question.