Question

A square circumscribes circle and another square is inscribed in this circle with one vertex at the point of contact. What is the ratio of the areas of the circumscribed and inscribed squares?

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

Answer 1

The correct option is B $2:1$

Let each edge of the square $ABCD=x$ units
Then area of square $ABCD$ $x^2$ sq units
For square $EFGH$ diagonal $EG=x$
$\therefore$ Side of square $EFGH$ $=\frac{x}{\sqrt{2}}$
$\therefore$ Area of square $EFGH$ $=\frac{1}{2}\times {\left(\text{diagonal}\right)}^2=\frac{1}{2}\times {\left(x\right)}^2=\frac{x^2}{2}$
$\therefore$ Required ratio $=\frac{\text{Area of square}ABCD}{\text{Area of square}EFGH}$
$=\frac{x^2}{x^2/2}=\frac{2}{1}=2:1$