AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

What will be the distance between two chords if they are on the opposite sides of the centre in a circle of radius 5 cm, and their lengths are 8 cm and 6 cm respectively?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

5cm

7cm

9cm

10cm

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that two chords are on the opposite sides of the centre in a circle of radius 5 cm, and their lengths are 8 cm and 6 cm respectively.
We have to find the distance between two chords.
Question Image

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

A L = 12 A B = 12 (8) = 4 cm

C M = 12 C D = 12 (6) = 3 cm

For right-angled ∆OLA,
Applying Pythagoras Theorem,

O A 2 = A L 2 + O L 2 ⇒ O L 2 = O A 2 − A L 2 = 52 − 42 = 25 − 16 = 9

Therefore OL = 3cm.
For right-angled

, Applying Pythagoras Theorem,

O C 2 = O M 2 + C M 2 ⇒ O M 2 = O C 2 − C M 2 = 52 − 32 = 25 − 9 = 16

Hence, OM = 4cm
Distance between the chords=OM+OL
=4+3
=7cm

So, the distance between the chords is 7cm.
Therefore, option 2 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!