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Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A)
256 cm2
(B) 128 cm2
(C) 642 cm2
(D) 64 cm2

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Solution


Given radius of circle r = OC = 8cm

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

which is equal to the diagonal of a square.

Let side of square be x

In right angled ΔABC, AC2=AB2+BC2
[By Pythagoras theorem]

(16)2=x2+x2

256=2x2

x2=128

Area of square =x2=128 cm2

Alternate method

Radius of circle (r) = 8cm

Diamter of circle (d) =2r=2×8=16 cm

Since square inscribed in circle,

Diagonal of the square = Diameter of circle

Now, Area of square =(Diagonal)22=(16)22=2562=128cm2

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