Book Online Demo
Check Your IQ
Try Test

Courses

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

Q.

AB is one of the direct common tangent of two circles of radii 12 cm and 4 cm respectively touching each other. Find the area of the region enclosed by the circles and the tangent.


     Question Image

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

24.78 c m 2  

b

18.53 c m 2  

c

19.54 c m 2  

d

14.8 c m 2   

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

It is given that the radii of two circles are PA=12cm and QB=4cm.
We have to find the area of the shaded region.
The area of a sector can be expressed as, A= θ 360 ° π r 2   . Here r   is the radius of a circle.
The required figure geometry is shown below,
     Question Image Then, by using the Pythagoras theorem from figure geometry,
     P Q 2 =P R 2 +R Q 2 ⇒ 16 2 = 8 2 +R Q 2 ⇒R Q 2 =192 ⇒RQ=8 3  cm   
The area of a trapezium, PABQ,
A= 1 2 AB PA+QB ⇒A= 1 2 8 3 12+4 ⇒A=64 3  cm    In the triangle PQR,   ∠Q= 180 ° −∠P   
⇒∠Q= 180 ° − 60 °     
⇒∠Q= 120 °  
Thus, the area of the region enclosed by the circles and the tangent isQuestion ImageThe required area is Question Image cm 2  .
Therefore, the correct option is 2.
 
Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

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 Books for IIT JEE
Best Books for NEET
score_test_img

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 Books for IIT JEE
Best Books for NEET
whats app icon
AB is one of the direct common tangent of two circles of radii 12 cm and 4 cm respectively touching each other. Find the area of the region enclosed by the circles and the tangent.