Question

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

• A. $1:2$
• B. $2:1$
• C. $3:1$
• D. $4:1$

Answer 1

The correct option is B $2:1$

Let cash edge of square $ABCD$$=x$ units
Then, area of square ABCD $x^2$
for square $EFGH$, diag, $HF=x$
$\Rightarrow$ side of square $EFGH=$ $x\sqrt{2}$
$\therefore$ Area of square $EFGH$ $={\left(\frac{x}{\sqrt{2}}\right)}^2=\frac{x^2}{2}$
$\therefore Requiredratio=x^2;\frac{x^2}{2}=2:1$