Assume we are given 3 segments in the plane so that there exists a line intersecting them. Regardless of their disjointness, can we always say that there is a line that is tangent to two of them while intersecting the third one?
(Here, a line is "tangent" to a segment if it passes through an endpoint.)
My idea is to take any line that intersects all three and firstly translate then rotate so that it is tangent to two while intersecting the third.
Do you see any flaw in this argument? Is there any counterexample?
Thanks!