Try this, ! the measure of a vertex angle of an isosceles triangle is 120º, the length of a leg is 8cm. find the length of a diameter of the circle circumscribed about this triangle. what is the radius in centimeters?

Check the picture below.

the triangle is an isosceles, so it has twin legs, and a base bottom.

the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.

if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.

so, anyhow, the rest is just a matter of using the 30-60-90 rule.

that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.