#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Click to Chat

1800-1023-196

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# If the radius of bigger circle is R.What will be the radius of smaller circle in terms of R?

## 2 Answers Priyansh Bajaj AskiitiansExpert-IITD
30 Points
10 years ago

Dear Vedanshu,

Solution:- Join origin (say, 'O') to the point (say, 'P') where both the circles are touching. This distance (i.e., OP) will be 'R' (since, it is the radius of bigger circle).

Now, let 'A' and 'B' be the point at which smaller circle is touching coordinate axes x and y respectively. And, center point of smaller circle be 'C'.

Then, OA = r, and OB = r. And, OACB is forming a square of side 'r'.

So, OC = √((OA)2 + (OB)2) = √2 r

Also, OP = OC + CP = √2 r  + r = (√2 +1) r = R

or, r = R / (√2 +1) [ANS]

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.

All the best!!!

Regards,
Askiitians Experts
Priyansh Bajaj

10 years ago

center  of smaller circle is at (r,r) ...distance from origen = (r2+r2)1/2 =21/2r

now the distance  from center of small sphere to point where it touches the big circle is r ...       (from diagram)

so the distance of point of contact from the origin is r + 21/2r=(21/2+1)r ......1

this total distance is the radius of bigger circle so

r(21/2+1) = R

r =  R/(21/2+1)

## ASK QUESTION

Get your questions answered by the expert for free