Answer:
16 cm
Step-by-step explanation:
Consider isosceles triangle ABC with vertex angle ACB of 120° and legs AC=CB=8 cm.
CD is the median of the triangle ABC. Since triangle ABC is isosceles triangle, then median CD is also angle ACB bisector and is the height drawn to the base AB. Thus,
∠DCB=60°
Consider triangle OBC. This triangle is isoscels triangle, because OC=OB=R of the circumscribed about triangle ABC circle. Thus,
∠OCB=∠OBC=60°
So, ∠COB=180°-60°-60°=60°.
Therefore, triangle OCB is equilateral triangle.
This gives that
OC+OB=BC=8 cm.
The diameter of the circumscribed circle is 16 cm.
