A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the… · ABC26GN4612

Let the radius of each of the circle and the semi-circle be $r$ units. Diagonal of the first square $=(2 r)$ units. Let the side of the second square be $a$ units. Then, $r^{2}=a^{2}+\left(\frac{a}{2}\right)^{2} \Rightarrow r^{2}=\frac{5 a^{2}}{4} \Rightarrow a^{2}=\frac{4 r^{2}}{5}$. ∴ Ratio of the areas of the two squares $$=\frac{\frac{1}{2} \times(2 r)^{2}}{a^{2}}=\frac{2 r^{2}}{\left(\frac{4 r^{2}}{5}\right)}=\frac{5}{2}=5: 2 .$$