Question

In the given figure, O is the centre of the circle, chords AB, CD and EF are equal whereas chords BC, DE and FA are separately equal. The angle AOC is equal to:

Options

• 80°

• 100°

• 90°

• 120°

Answer 1

120°

Explanation:

Given,

Chords AB, CD and EF are equal.

∴ ∠AOB = ∠COD = ∠EOF = x (let)

Chords BC, DE and FA are equal.

∴ ∠BOC = ∠DOE = ∠AOF = y (let)

From figure,

⇒ ∠AOB + ∠COD + ∠EOF + ∠BOC + ∠DOE + ∠AOF = 360°

⇒ x + x + x + y + y + y = 360°

⇒ 3x + 3y = 360°

⇒ 3(x + y) = 360°

⇒ x + y = `(360°)/3`

⇒ x + y = 120°

From figure,

∠AOC = ∠AOB + ∠BOC = x + y = 120°.