Arun
Last Activity: 6 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
