What is the perimeter of a square inscribed in a circle of radius $5 ext{ cm}$?

Question

What is the perimeter of a square inscribed in a circle of radius $5 	ext{ cm}$?

Accepted Answer

**Solution:**

1. The diagonal of the square is equal to the diameter of the circle. Given radius $r = 5 	ext{ cm}$, diameter $d = 2r = 10 	ext{ cm}$.

2. Using the Pythagorean theorem for the square's diagonal:
   $$s^2 + s^2 = d^2 \implies 2s^2 = 10^2 = 100 \implies s^2 = 50 \implies s = 5\sqrt{2} 	ext{ cm}$$

3. The perimeter of the square is:
   $$P = 4s = 4 	imes 5\sqrt{2} = 20\sqrt{2} 	ext{ cm}$$

**Answer:** $20\sqrt{2} 	ext{ cm}$

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