Question

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:

Options

• 4 : 7

• 5 : 4

• 7 : 4

• 4 : 5

Answer 1

7 : 4

Explanation: 

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

⇒ `(OD)/(OB) = (OA)/(OC)`

⇒ `(OD)/(OB) = 4/7`

⇒ `(OB)/(OD) = 7/4`

⇒ OB : OD = 7 : 4