Question : What is the perimeter of a square inscribed in a circle of radius 5 cm?
Option 1: $20 \sqrt{2}\ \mathrm{~cm}$
Option 2: $40\sqrt{2}\ \mathrm{~cm}$
Option 3: $30\sqrt{2}\ \mathrm{~cm}$
Option 4: $10\sqrt{2}\ \mathrm{~cm}$
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Correct Answer: $20 \sqrt{2}\ \mathrm{~cm}$
Solution :
The radius of the circle, $r$ = 5 cm
Let the side of a square be $a$.
Diameter of the circle = 2 × $r$ = 2 × 5 = 10 cm = Diagonal of a square
Also, the diagonal of a square = $a\sqrt2$
⇒ $10=a\sqrt2$
⇒ $a=5\sqrt2\ \text{cm}$
The perimeter of a square = $4a=4×5\sqrt2=20\sqrt2\ \text{cm}$
Hence, the correct answer is $20\sqrt2\ \text{cm}$.
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