The line segments do not look like a proposed arc is tangential, that is my question. If so then the end points of the 2 straights will move. Adopting one of the mid points as a control.
Actually,
In actual work, there is a small probability that random fold lines like the original poster will appear.
Generally, it is as shown in the figure below. For some reasons, the arc segment becomes many small segments. Such a figure can be fitted with an accuracy of 99.999%, which means there is no need to deal with tangency. Condition
The following picture can also be processed fully automatically