There is no such thing as 'the' tangent point here. This is a spline on a spherical surface ending tangent in an arc.
I assume you are looking the first point where the spline is within modeling tolerance of the plane. You can find that by creating an intersection point between the edge and the plane.
You will have to pick where indicated. The spline is almost tangent at many other locations.
If you still have the original trimming geometry then that would probably make it a lot easier to find the correct location.
I hope I understood your request correctly.
Sorry for the ambiguous description of the problem. What you talk about is exactly what I want.
It works! And it's magic that an intersect point can be produced even when the edge has a major part lying on the datum plane.