where r is the geometric ratio.
So your conditions are
Thus we have two equations in two unknowns.
The first condition reads:
and the second reads
There are a variety of ways to attack this. This is one:
Solve the top equation for :
and insert it into the bottom equation:
And finally, multiply both sides by :
This is a quadratic in r, which I am sure you can solve.
Note: For good or for ill I get that r is a complex number. I see no reason why this shouldn't be so, but I doubt you expected it. As I am not familiar with seeing problems like this turn out to be complex, I am wondering if there isn't some kind of typo?