In the above figure, if OA=x and ∠AOB=120∘, find the length of chord AB in terms of x.
Let the length of chord AB be a units.
Using cosine rule we get,
cos120=x2+x2−a22x2
−12=2x2−a22x2
−x2−2x2=−a2
a=x√3
Hence, length of chord AB is x√3 units.