Question

Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A) $256c{m}^2$
(B) $128c{m}^2$
(C) $64\sqrt{2}c{m}^2$
(D) $64c{m}^2$

Answer 1

Given radius of circle r = OC = 8cm

$\therefore$ Diameter of the circle $=AC=2\times OC=2\times 8=16cm$

which is equal to the diagonal of a square.

Let side of square be x

In right angled $\Delta ABC,A{C}^2=A{B}^2+B{C}^2$
[By Pythagoras theorem]

$\Rightarrow (16{)}^2=x^2+x^2$

$\Rightarrow 256=2x^2$

$\Rightarrow x^2=128$

$\therefore$ Area of square $=x^2=128c{m}^2$

Alternate method

Radius of circle (r) = 8cm

Diamter of circle (d) $=2r=2\times 8=16cm$

Since square inscribed in circle,

$\therefore$ Diagonal of the square = Diameter of circle

Now, Area of square $=\frac{(Diagonal{)}^2}{2}=\frac{(16{)}^2}{2}=\frac{256}{2}=128c{m}^2$