20.91 A square with an area of 40 is inscribed in a semicircle. If another square is inscribed in a full circle of the same radius, then the area of this square is 
(A) 80.
(B) 100.
(C) 120.
(D) 160.
(E) 200.
(10th American High School Mathematics Examination, 1959)
[Solution] Let the side length of square $ABCD$ be $a$, then the radius of $\odot O$
$$
R=\sqrt{a^{2}+\left(\frac{a}{2}\right)^{2}}=\frac{\sqrt{5}}{2} a .
$$

The diagonal length of square $EFGH$ is $2R$, then
$$
S_{\square EFGH}=\left(\frac{2 R}{\sqrt{2}}\right)^{2}=\frac{5 a^{2}}{2}=100 .
$$

Therefore, the answer is $(B)$.