A secant line through two points between the red and magenta points of tangency of the curve and the hyperboloid meets the hyperboloid in 2 points, so there are two real lines that meet these three tangent lines and such a secant line. This gives two flags l contained in H where l meets the three tangent lines and H meets the rational normal curve in the two points of secancy.

    Let us now consider secant line that meets two different arcs.