Answer:
Pretend that H is the midpoint of AB, connect O and H
=> OH is the median of ΔOAB
Since we know that OA = OB => ΔOAB is an isosceles triangle
=> OH is also the height of ΔOAB
=> ∠OBA = ∠OAB = (180° - ∠AOB)/2 = (180° - 120°)/2 = 60°/2 = 30°
Now look at ΔOHB (that you create by connecting O and H)
We have:
cos30° = BH/OB
=> BH = cos30° · OB = √3/2 · x = (√3 x)/2
Because we have H as the midpoint of AB, we know that:
AB = 2 · BH = 2 · (√3 x)/2 = √3 x
So the answer is B