Question

Chord AB subtends ∠AOB = 60° at centre. If OA = 5 cm then find the length of AB (in cm).

Answer 1

∠AOB = 60°
OA =radius = 5 cm 
OB = 5 cm

Since OA=OB, it is a isosceles triangle.
∠ABO = ∠BAO 

In the triangle,
∠AOB +∠ABO + ∠BAO = 180° 
So ∠ABO + ∠BAO = 180-60 = 120 
∠ABO = 120/2 = 60 and 
∠BAO = 60 

SO it is an equilateral triangle. So all sides are equal.
Hence AB = 5cm

Answer 2

Let the triangle be AOB where ∠AOB = 60°
Then we have AO = BO = 5 cm
Since Δ AOB is a isosceles triangle.
∠ABO = ∠BAO = (180-60)/2 = 60  degree
Hence we have, ΔAOB is an equiangular triangle hence an equilateral triangle where all sides are equal ⇒ AO = BO = AB = 5 cm
Length of AB is 5 cm