Question

A square is inscribed in a circle of radius $2$ cm. Side of the square in cm is:

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

Answer 1

The correct option is B $2$ $\sqrt{2}$

Square is inscribed in a circle therefore Diagonal of square is the diameter of a circle.

By the property of square all four sides are equal in length.

So, $AB=BC=CD=DA$.

Also, $\angle ADC={90}^{\circ }$.

By applying Pythagoras theorem;

${AC}^2={AD}^2+{CD}^2$;

But $AD=CD$.

Thus, $A{C}^2=A{D}^2+A{D}^2$

Hence, $AC=\sqrt{2}AD$

$AD=\frac{1}{\sqrt{2}}AC$

$AD=\frac{1}{\sqrt{2}}4$

$AD=2\sqrt{2}$cm

therefore side of square is $2\sqrt{2}$cm

option B is answer.