Question

AB and CD are two chords of a circle which intersect at a point O inside the circle. It is given that, AB = 10 cm, CO= 1.5 cm and DO = 12.5 cm. What is the ratio between the larger and smaller among AO and BO?

Options:
1. 3 : 2
2. 4 : 1
3. 7 : 3
4. 3 : 1
Correct answer: 3 : 1
​

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R:-}}}}$

Answer:3:1

Step-by-step explanation:

By the property of circle when 2 chords intersect each other

AO ×OB=CO ×OD

(OB =10 -AO)

10-OB ×OB=1.5×12.5

OB^2-10 OB +18.75=0

on solving the equation you will get x 2.5i.e OB

And AO=10-2.5=7.5

The ratio of 7.5/2.5=3:1

♥️Please mark it as♥️

$\huge\underline\mathcal\red{Brainliest}$

Answer 2

Step-by-step explanation:

By the property of circle when 2 chords intersect each other

AO ×OB=CO ×OD

(OB =10 -AO)

10-OB ×OB=1.5×12.5

OB^2-10 OB +18.75=0

on solving the equation you will get x 2.5i.e OB

And AO=10-2.5=7.5

The ratio of 7.5/2.5=3:1

♥️Please mark it as♥️