Chords AB and CD of a circle intersect each other at point O such that OA : OC = 4 : 7. Then OB : OD is equal to :

1. 4 : 7

2. 5 : 4

3. 7 : 4

4. 4 : 5

Given,

OA : OC = 4 : 7

We know that,

If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal.

From figure,

⇒ OA × OB = OC × OD

⇒ $\dfrac{OD}{OB} = \dfrac{OA}{OC}$

⇒ $\dfrac{OD}{OB} = \dfrac{4}{7}$

⇒ $\dfrac{OB}{OD} = \dfrac{7}{4}$.

⇒ OB : OD = 7 : 4.

Hence, Option 3 is the correct option.