Question

In the given figure, O is centre of the circle and chord AB : chord CD = 5 : 3. If angle DOC = 60°; then ∠AOB is:

Options

• 120°

• 75°

• 100°

• 80°

Answer 1

100°

Explanation:

• In a circle, the lengths of chords are directly proportional to the angles they subtend at the centre.
• We are given the ratio of the chords as chord AB : chord CD = 5 : 3, which means the ratio of their central angles is also ∠AOB : ∠DOC = 5 : 3.
• We are given that ∠DOC = 60°. Let ∠AOB = x. Using the proportion:
  
  `\frac{x}{60^\circ} = \frac{5}{3}`
  3x = 5 × 60°
  3x = 300°
  x = `\frac{300^\circ}{3} = 100^\circ`

Thus, ∠AOB = 100°.