Its pretty straight forward in NX and its parametric too. Please find attached the solution. Since i dont know which version of NX you are using I made it in parasolid.
The method is as follows.
1. project your sketch on the ID of the cylinder.
2. Devide the ID face with the projected curves.
3. Make a thicken sheet using the devided face (-50 and +50) and subtract.
You are done.
The trick is thicken sheet which creats a solid always perpendicular to face.