The side of an isosceles triangle is 4, the apex angle opposite the base is 120, find the diameter of the circle around this triangle.

The sum of the angles of the triangle is 180 degrees, so 180-120 = 60 degrees remains for two angles at the base of the triangle. Since the triangle is isosceles, the angles at the base are equal, so each of them is equal to 30 degrees.
The radius of the circumscribed circle is calculated by the formula R = a / (2 * sin (A)), where the angle A is opposite to side a. Hence R = 4 / (2 * sin (30)) = 4.
D = 2 * R = 8.
Answer: 8 cm.