Curve on a Surface?

In the attached file I have a surface (highlighted) with a line at one end. I would like to create two curves on the surface running from the opposite end (marked by points) to (and tangent to) the curve. Is there some simple way to approach this?

The ultimate goal is to trim the surface (or create a new surface from the curves)

Problem Curve on Surface.3dm (3.0 MB)

Hello - Match an edge curve to the line, then Pull with Loose=Yes the the surface.