You have three variables and two independent equations:

3x + 2y + z = π/4

4x + 4y + z = 1

To have a unique solution, you need three equations. My guess is that you can't form the third equation without using the facts that these are actual circles. It may be possible to twist the shape a little preserving the two equations above.

Anyway, you an find y/2 using trigonometry. That would be the third equation.