Convex Polygons and Common Transversals
Peter I. Hajnal, László I. Szabó, Вилмос Тотик · American Mathematical Monthly · 2015
It is shown that if two planar convex n-gons are oppositely oriented, then the segments joining the corresponding vertices have a common transversal. A different formulation is also given in terms of two cars moving along two convex curves in opposite directions. Some possible analogs in 3-space are also considered, and an example is shown that the full analog is not true in this setting.