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

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KollegeApply · Accepted Answer

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. $\therefore$ Diameter of the circle = AC = 2 $\times$ OC = 2 $\times$ 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] $\Rightarrow$ (16)2 = x2 + x2 $\Rightarrow$ 256 = 2x2 $\Rightarrow$ x2 = 128 $\therefore$ Area of square = x2 = 128 cm2 [Solution diagram: 258734_solution_1.png]

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