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

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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