Question

In the given figure, O is centre of the circle and ABC is an equilateral triangle, then ∠AOB is equal to:

Options

• 105°

• 90°

• 60°

• 120°

Answer 1

120°

Explanation:

• Since ΔABC is an equilateral triangle inscribed in the circle, all its sides (AB, BC, and CA) are equal in length.
• Equal chords subtend equal angles at the centre of the circle. Therefore, the central angles ∠AOB, ∠BOC, and ∠COA are all equal to each other.
• Since the sum of angles around a point at the centre is 360°:
  ∠AOB + ∠BOC + ∠COA = 360°
  3 × ∠AOB = 360°
  ∠AOB = `\frac{360^\circ}{3} = 120^\circ`