The length of a circle circumscribed about a square is 8pi cm. find the perimeter of the square.
| April 28, 2021 | education
The diagonal AC of the square ABCD is the diameter of the circumscribed circle around it.
The circumference is: L = 2 * π * R = 8 * π.
R = 8 * π / 2 * π = 4 cm.
Triangle AOB is rectangular and isosceles, then AB ^ 2 = 2 * R ^ 2.
AB = R * √2 = 4 * √2 cm.
Then Ravsd = 4 * AB = 16 * √2 cm.
Answer: The perimeter of the square is 16 * √2 cm.
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