The side of an equilateral triangle is 3 cm. Find the circumference of the circle around it?

Since the triangle is regular, the center of the circle circumscribed around it coincides with the intersection point of the bisectors, medians and heights of the regular triangle.

In a regular triangle, the medians of the triangle, at the intersection point, are divided in a ratio of 2: 1, counting from the vertex BO / OD = 2/1, then BO / BD = 2/3.

Since in a regular triangle all angles are 60, then Sin60 = BD / AB.

BD = Sin60 / AB = (√3 / 2) / 3 = 3 * √3 / 2.

Then BО / 3 * √3 / 2 = 2/3.

BO = (2/3) * (3 * √3 / 2) = √3.

Then the circumference is: L = 2 * n * R = 2 * n * √3.

Answer: The radius of the circle is 2 * n * √3.