Question

The area of a square inscribed in a circle of radius 8 cm is :

• A. $64c{m}^2$
• B. $100c{m}^2$
• C. $125c{m}^2$
• D. $128c{m}^2$

Answer 1

The correct option is D $128c{m}^2$

Let $ABCD$ be the square inscribed by the circle.

$\therefore OA=OB=OC=OD$

$ABC$ is a right angled triangle, as $OA=8,OB=8$

$AB=8+8=16$

According to Pythagoras theorem,

Square of hypotenuse = Sum of squares of other two sides.

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

As ABCD is a square all the sides are equal, $AB=BC$

$A{C}^2=2A{B}^2$

${16}^2=2A{B}^2$

$\therefore AB=8\sqrt{2}$

therefore side of the square $=8\sqrt{2}$

Area of square $=(8\sqrt{2}{)}^2=128c{m}^2$