Question

AB and CD are chords of a circle with centre O, ∠AOB = 60° and angle ∠COD = 45°: the ratio between the lengths of chords AB and CD is ______.

Options

• 3 : 4

• 4 : 3

• 7 : 4

• 7 : 3

Answer 1

AB and CD are chords of a circle with centre O, ∠AOB = 60° and angle ∠COD = 45°: the ratio between the lengths of chords AB and CD is 4 : 3.

Explanation:

For a chord, length × sin `(θ/2)`.

So,

`"AB"/"CD" = "sin30"^circ/"sin22.5"^circ = 0.5/0.3827 ≈ 1.3`

Therefore,

AB : CD ≈ 4 : 3

So, the answer is 4 : 3.