The side of the circumscribed triangle is 3 cm. Find the side of the regular 4-gon circumscribed about the same circle.

Apparently, the described triangle is equilateral. The circle is inscribed in this triangle. The radius of a circle inscribed in a regular triangle is found by the formula:
r = a / 2√3 = 3 / 2√3 = √3 / 2 (cm).
A regular quadrilateral that is circumscribed around a circle is a square.
Find the side of the square:
r = a / 2 → a = 2 * r = 2 * √3 / 2 = √3 (cm).
Answer: the side of the described square is √3 cm.

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