Question

Find the area of a square that can be inscribed in a circle of radius $8cm.$

Answer 1

Radius of circle $=8cm$
Diameter $=8\times 2=16cm$

The diameter of circle $=$ diagonal of square $=16cm$

$BD=16cm$

Since, $CD=BC=side$, as all sides of the square are equal.

Applying Pythagoras theorem, we have

$D{C}^2+C{B}^2=B{D}^2$

$\Rightarrow 2(side{)}^2=16\times 16$

$\Rightarrow (side{)}^2=\frac{16\times 16}{2}=16\times 8=128c{m}^2$

Area of square $=(side{)}^2=128c{m}^2$