Question

In the given figure, O is centre of the circle. Chord BC = chord CD and angle A = 80°. Angle BOC is:

Options

• 120°

• 80°

• 100°

• 160°

Answer 1

80°

Explanation:

Given,

Chord BC = chord CD

∴ ∠BOC = ∠COD = x (let)

From figure,

∠BOD = ∠BOC + ∠COD = x + x = 2x

We know that,

The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

⇒ ∠BOD = 2∠BAD

⇒ 2x = 2 × 80°

⇒ x = 80°