# A regular quadrangle with a perimeter of 16 meters is inscribed in a circle. What is the radius of the circle?

September 30, 2021 | education

| Since the quadrilateral ABCD is regular, it is a square.

Let us determine the length of its side through the perimeter of the square.

AB = AD = BC = CD = P / 4 = 16/4 = 4 cm.

Triangle ABD is rectangular, then by the Pythagorean theorem, we determine the length of the diagonal of the square. BD ^ 2 = AB ^ 2 + AD ^ 2 = 2 * AB ^ 2 = 2 * 16 = 32.

ВD = √32 = 4 * √2 cm.

The diagonal of a square inscribed in a circle is its diameter, then R = ВD / 2 = 4 * √2 / 2 = 2 * √2 cm.

Answer: The radius of the circle is 2 * √2 cm.

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