Answer:
a) A₁ /A₂  =  r₁² / (r₂²   - r₁²)
b) A₂ /A₃  = (r₂²   - r₁²) / (r₃²   - r₂²) 
Step-by-step explanation:
We have Circle 1  and area  A₁  
Area of circle 2 outside circle 1     =  A₂
Area of circle 3 outside circle 2    = A₃
On the other hand we have
A₁  = π*r₁²   area of circle 1
A₂´ =  π*r₂² area of circle 2
A₃´ = π*r₃²  area of circle 3
All areas in cm²
a) A₁ /A₂         
A₁  =  π*r₁²
According to problem statement  A₂  = π*r₂²  -   A₁
 A₂  =  π*r₂²  -   π*r₁²      ⇒         A₂  =  π* (r₂²   - r₁²)
Then  A₁ /A₂  =   π*r₁² / [π* (r₂²   - r₁²)]
A₁ /A₂  =  r₁² / (r₂²   - r₁²)
b)  A₂ /A₃        
A₂  =   π* (r₂²   - r₁²)
And
A₃   =  π* (r₃²   - r₂²)
Therefore
 A₂ /A₃  =   π* (r₂²   - r₁²) / π* (r₃²   - r₂²)  ⇒  A₂ /A₃  = (r₂²   - r₁²) / (r₃²   - r₂²) 
A₂ /A₃  = (r₂²   - r₁²) / (r₃²   - r₂²)