In an isosceles triangle ABC, angle B = 120 ‘. The radius of the circle circumscribed about

In an isosceles triangle ABC, angle B = 120 ‘. The radius of the circle circumscribed about the triangle is 2cm, find the side AB.

Let’s build the radii OA and OC. In an isosceles triangle AOC, we will construct the height and median OH. AH = CH.

In an isosceles triangle AOС, we will construct the height, bisector and median of ВН. AH = CH.

Then points B, H and O lie on one straight line, and BO is the radius of the circle.

Triangle AOB is equilateral, OA = OB = 2 cm, angle ABO = 120/2 = 60, then triangle AOB is equilateral, which means AB = R = 2 cm.

Answer: The length of the AB side is 2 cm.