Question

In the given figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of inner square? Give reasons for your answer.

• A. True
• B. False

Answer 1

The correct option is B False

Let the side of the smaller square is a units and that of bigger square is $b$ units.
Diameter of circle $=d$
So, diagonal of square $EFGH=d$
Then, by Pythagoras theorem,
$a^2+a^2=d^2$
$\Rightarrow 2a^2=d^2$
$\Rightarrow a^2=\frac{d^2}{2}$
$\therefore$ Area of smaller square $=a^2=\frac{d^2}{2}$
Side of outer square $=b=$ Diameter of circle
$\therefore$ Area of larger square $=b^2=d^2$
$=>$ Area of outer square $=2$ Area of smaller square
So, the given statement is false.