Re: A square is inscribed in a circle. The diameter of the circle is equ
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08 Mar 2025, 00:53
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).