# The radius of the circumscribed circle of a regular hexagon is 2√3. Find the radius of the circle inscribed in this hexagon.

May 26, 2021 | education

| The radius of a circle circumscribed about a regular polygon is determined by the formula:

R = a / (2 * Sin (180 / N).

2 * √3 = a / 2 * Sin30 = a / 1.

a = 2 * √3 cm.

The radius of the inscribed circle in a regular polygon is:

r = a / 2 * tg (180 / N) = 2 * √3 / 2 * tg30 = 3 cm.

Answer: The radius of the inscribed circle is 3 cm.

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