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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