Get curve on surface of brep

Hello.
I have the following problem: there is a curved surface built using two segments of a circle with different radius and different height position. I need to build a curve on the surface by two variants:

  1. more complicated - with an offset (can be different) from the corners on the diagonal.
  2. simple - from one corner to the other on the diagonal. In general, it is even clear that you can find the center of the curves, draw a line between them to find the middle of this curve, but what to do next, what tool to use I do not know.
    Maybe who has faced such a problem and knows the solution?

    Get_curve_on_brep.gh (3.1 KB)

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Thank you for reply, but it doesn’t what i want to get.
If we look at the result in the XZ plane, we see that the curve is stretched perpendicularly (along the normal) to the surface, whereas I need it to be stretched horizontally along the XY plane (then the lines will coincide in the XZ plane).
image

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I appreciate your prompt replies :pray:. But it seems that I don’t understand final result clearly myself which i want. :grinning: I’ll come back later with an understanding of what the line should be on the surface

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