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

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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