Question

In a circle, O is its centre and AB, CD are B its two chords. If AB : CD = 3 : 2, then ratio between ∠AOB and ∠COD is ______.

Options

• 1 : 1

• 3 : 2

• 2 : 5

• 3 : 5

Answer 1

In a circle, O is its centre and AB, CD are B its two chords. If AB : CD = 3 : 2, then ratio between ∠AOB and ∠COD is 3 : 2.

Explanation:

• In a circle, equal chords subtend equal angles at the centre, and the central angles are proportional to the lengths of their corresponding chords.
• Given that the ratio of the chord lengths is AB : CD = 3 : 2, the ratio of the angles subtended by them at the centre, ∠AOB : ∠COD, is directly proportional to their lengths.

Therefore, the ratio between ∠AOB and ∠COD is 3 : 2.