Question

In the given figure, a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Find the ratio of areas of the bigger square to the smaller square.

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

Answer 1

Answer: (D)

$2:1$

$PQRS$ is a square inscribed in a circle of diameter

$SQ=d$ which in turn has been inscribed in the square $ABCD$.

To find out whether $ar.ABCD=4\times ar.PQRS$ or not.

$SQ=d$ is the diagonal of the square $PQRS$

Since the diameter of a circle circumscribing a square $=$ diagonal of the same square.

$\therefore$ Any side of $PQRS=PQ=\sqrt{\frac{d^2}{2}}$

$\therefore ar.PQRS=\frac{d^2}{2}$

Again $SD=d=$ one side of $ABCD=AD$.

$\therefore ar.ABCD={AD}^2=d^2$

So, $\frac{ar.ABCD}{ar.PQRS}=\frac{d^2}{\frac{d^2}{2}}=2$

Ratio of area of outer square to the area of inner square is $2:1$.

Hence, option D is correct.