Hi tmoria!

You do have a constraint.

Since the segments a, b, and c are in the same plane and bounded by 2 lines, you get the constraint: a-2b+c=0.

So let's suppose that a and b are known, then we require that:

$\displaystyle c=2b-a \qquad (1)$

Let's call the unnamed line segments A, B, and C.

Then we can set up the system of equations:

$\displaystyle A-2B+C=0$

$\displaystyle A^2+a^2=R^2$

$\displaystyle B^2+b^2=(R+d)^2$

$\displaystyle C^2+c^2=(R+2d)^2$

We have 4 equations with 5 unknowns.

That means we can choose one unknown for free.

So let's pick A ourselves, then we can solve the system getting:

$\displaystyle R=\sqrt{a^2 + A^2}$

$\displaystyle d=\frac{b-a}{a}R$

$\displaystyle B=\frac b a A$

$\displaystyle C=\frac c a A$

A solution like this is easiest to calculate with Wolfram|Alpha.