Draw vertical line from knot to line

This is something that is simple to do in Rhino, but unfortunately I have to do it a couple of hundred times (and will likely have to do it again in the future). So I would LOVE to automate it if possible.

I have a series of circles that are below to a curve, all in the same plane. I need to draw lines from the left and right knots (or tangents) of the circles, vertically, to intersect the curve above. I attached a screen shot that should make it clear: the cyan curves are what I have to start, the red lines are what I need to draw.

(To do this manually I just turn on knot snaps, and use the shift key to constrain the line vertically.)

I can't seem to even figure out how to start this in GH. Anyone have ideas?