Thank you for registering.

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

Please check your email for login details.
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

There are 3 semicircles touching each other internally and one circle touching two of them externally and third one internally. Radius of the complete circle (in its lowest form) is p/q p, q belong to N then p + q is ?

There are 3 semicircles touching each other internally and one circle touching two of them externally and third one internally. Radius of the complete circle (in its lowest form) is 
p/q
p, q belong to N
then p + q is ?

Question Image
Grade:10

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
 
let center of bigger semicircle(radius=3) is R1 ,the next bigger one (radius=2) is R2 and the smaller one(radius=1) is R3 and complete circle one is R (assume its radius is r )
Now consider the triangle R2 R3 R and draw a line from R to R1 it acts as a cevian on this trisngle lengths of triangle
R2 R3 = 3
R2 R =2+R
R3 R=1+R
R1 R=3-R  [bigger circle is normal and complete circle are same so radius of both coincide]
R2 R1=1
R3 R1=2
now apply cosine rule at point R1
(2+r)2-12-(3-r)2/2*1*(3-r)   = -[(1+r)2-22-(3-r)2/2*2*(3-r)]
solving this we get   r=  12/14=6/7
p+q=13
 
Regards
Arun

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free