# A circle of 6 cm is described around the square. A) find the radius of the circumscribed circle

August 31, 2021 | education

| **A circle of 6 cm is described around the square. A) find the radius of the circumscribed circle b) the side of the regular triangle circumscribed about the given circumference**

The radius of the circle in which the square is inscribed is half the diagonal of this square. From a right-angled triangle ABC, AC ^ 2 = AB ^ 2 * BC ^ 2 = 36 + 36 = 72.

AC = √72 = 6 * √2 cm.

R = ОА = АС / 2 = 6 * √2 / 2 = 3 * √2 cm.

The radius of a circle inscribed in a regular triangle is: R = a * √3 / 6, where a is the side of the triangle.

Then KP = 6 * R / √3 = 6 * 3 * √2 / √3 = 6 * √6 cm.

Answer: The radius of the circle is 3 * √2 cm, the side of the triangle is 6 * √6 cm.

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