Hi Nick, another possibility could be to draw a circle off to the side a bit, then select the circle and run Construct > Sweep, then select the path curve and you will then have a tube object that follows along your path curve.
Now with the tube in place, select the tube and the face that you are interested in and run Construct > Curve > Isect - that will calculate an intersection curve between the tube and the face and that looks like the kind of result you want.
See attached 3DM file with the tube and intersection result in place.
- Michael
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