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Question
The area of the square that can be inscribed in a circle of radius 8 cm is ______.
Options
256 cm2
128 cm2
`64sqrt(2)` cm2
64 cm2
Solution
The area of the square that can be inscribed in a circle of radius 8 cm is 128 cm2.
Explanation:
Given, radius of circle, r = OC = 8 cm.
∴ 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
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