As given in the question, in the figure above, square $\(A B C D\)$ is inscribed in circle of radius 10 and the diagonal of the square is equal to the diameter of the circle.

Let the side of the square be ' $\(a\)$ '
The diameter of the circle is $\(2 \times\)$ radius $\(=2 \times 10=20\)$ which is same as diagonal of the square, so we get $\(\mathrm{a} \sqrt{2}=20 \Rightarrow \mathrm{a}=10 \sqrt{2}(\because\)$ Diagonal in a square is $\(\sqrt{2}$ times the side $)\)$

So, the area of the square is Side $\({ }^2=a^2=(10 \sqrt{2})^2=200\)$
Hence the answer is (D).