A circle with a radius of 2 \ 3 is inscribed in a regular triangle, which is equal to the radius of the inscribed circle

The center of the inscribed circle in a triangle is the intersection point of the bisectors of the triangle.

Since the triangle ABC is equilateral, the bisectors are also the medians of the triangle.

The medians of the triangle at point O are divided in the ratio of 2/1, then OB = 2 * OH = 2 * 2/3 = 4/3 cm.

In an equilateral triangle, the center of the incircle and the circumcircle coincide.

Then R = ОВ = 4/3 cm.

Answer: The radius of the circumscribed circle is 4/3 cm.