The four circles will have radii increasing in a geometric progression. Let’s call them 1, a, a^2, a^3. We also know that a+a^2=a^3. a is not equal to 0, so we can divide throughout: 1+a=a^2
This is a quadratic and the positive solution is that a=phi.
The second circle will have a radius of phi, the golden ratio, 1.618…, (sqrt(5)+1)/2.