Question

A circle is inscribed in a square and then a smaller square is inscribed in the circle. The ratio of the area of the smaller square to that of the larger square is

• A. $1:4$
• B. $\sqrt{2}:2$
• C. $1:2$
• D. $1:\sqrt{2}$
• E. $2:3$

Answer 1

The correct option is C $1:2$

Let the radius of smaller circle be $r$, then length of side of larger square is $2r$ and the length of side of smaller square is $\sqrt{2}r$.
The ratio of area of smaller square to larger square is $\frac{4r^2}{4{\left(\sqrt{2}r\right)}^2}=\frac{1}{2}$