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

Q.

In given figure, two circles with centers A and B of radii 20 cm and 8 cm touch each other internally. If the perpendicular bisector of segment $AB$ meets the bigger circle in $P$ and $Q,$ find the length of $PQ$ .

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

a

493 cm

b

494 cm

c

492 cm

d

491 cm

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

Given that two circles with centers A and B of radii 20 cm and 8 cm touch each other internally.
We have to find the length of PQ.
The Pythagoras theorem relates the sides of a triangle and is expressed as the square of the hypotenuse side is equal to the sum of squares of the other two sides.
The required figure geometry is shown below,
Question Image

Question Image

In the figure, Since PQ is perpendicular bisector on AB. So,

A B = A C − B C ⇒ A B = 20 − 8 ∴ A B = 12 cm

The triangle ADP is the right triangle at D. Thus,

A P 2 = P D 2 + A D 2 ⇒ 202 = P D 2 + 62 ⇒ 400 − 36 = P D 2 ⇒ P D = 291 cm

Since PQ is a chord which intersects AC that passes through the center so AC is perpendicular bisector on PQ. Thus, PD = QD Therefore,

P Q = P D + Q D ⇒ P Q = 2 P D ⇒ P Q = 2 (291) ⇒ P Q = 491 cm

The length of PQ is

491 cm

.
Therefore, the correct option is 1.

Watch 3-min video & get full concept clarity

courses

No courses found

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

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!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

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

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

gplay

mentor

Download the App

gplay

personalised 1:1 online tutoring