Q. 84.3( 15 Votes )

# The area of the square that can be inscribed in a circle of radius 8 cm is

Given: Radius of circle = 8 cm

To find: Area of the square

Explanation:

Let r be the radius of circle = OC = 8 cm.

Diameter of the circle = AC = 2 × OC = 2 × 8 = 16 cm

Let a be the side of the square.

Now, according to the given condition,

Diagonal of square = Diameter of the circle.

Now in right angled triangle ACB,

(AC)2 = (AB)2 + (BC)2

(By Pythagoras theorem)

(16)2 = a2 + a2

256 = 2a2

a2 = 128

Area of the square = a2 = 128 cm2

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