Hyperboloid Through the Three Tangent Lines

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The lines meeting these three lines form a ruling of a hyperboloid of one sheet containing the three tangent lines. Each intersection of this hyperboloid with a fourth line gives a line meeting all four. In this geometric context, the Theorem of Mukhin, Tarasov, and Varchenko is
	equivalent to the following geometric statement: Any line tangent to the rational normal curve at a real point meets the hyperboloid in two real points.     It is not hard to believe this, as the rational normal curve loops around inside the hyperboloid.

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