**AB is a chord of a circle having centre O. If ∠AOB = 60°, then prove that the chord AB is of radius length.**

###### Answers:

Here, OA = OB = r [radii of same circle]

⇒ ∠A = ∠B —– (i)

In ΔOAB,

∠O + ∠A + ∠B = 180°

⇒ 60° + ∠A +∠A = 180° [using eq. (i)]

⇒ ∠A = 60°

Thus ∠O = ∠A = ∠B = 60°

⇒ ΔOAB is an equilateral triangle .

⇒ AB = OA = OB = r Hence proved.