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Or, even simpler, just make a point, and make it coincident with the two curves you want to be tangent to each other. Then just click the point to get its location.
One thing I do is use a construction line with a Horizontal/Vertical constraint and then make it Tangent to the spline. That gives you the apex point immediately without moving your spline geometry around too much.
Easy: Leave the spline in it's own sketch, els i'll move. Make a new sketch on the same sketch plane. There, make a point on the spline somewhere, and draw a mid point line on that point. Make the line tangent with the spline. Then constrain the line to horizontal. That'll be the spline apex point. I sometimes use that with airfols and mold making. The trick is, that the line in the second sketch will not move your spline.
(Sorry for the late answer, this message got stuck until now)