Define

where r is the geometric ratio.

So

and

So your conditions are

and

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?

-Dan