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.