How to find point on arch to draw vertical line to?

Grasshopper
1

I am lost, or more truthfull! ( an idot ) can some one help me to find the location on a moving arch. So i can draw the vertical line to stop at the arch!
I want to eventualy draw multipal spaced vertical lines within the arch, and to adjust the arch, befor sending to Rhino!

GH%20trim%20test
GH%20trim%20test1546×646 129 KB

2

Here is one example. There are many ways.

ArcLineExample.gh (6.8 KB)

3

Also here with multiple lines.

ArcLineExample_MultipleLines.gh (9.4 KB)

4

Thank you so much, You have no idea how many days i have spent with a numb head over this.
I have been all over the lawn, ( grasshopper ) ! trying to fathom this out.
thank you