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:

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

Then we can set up the system of equations:

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:

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