Q. 84.3( 15 Votes )

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

Answer :

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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