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).