Sharygin CR 2019 P23
Source: Sharygin CR 2019 P23 (Grade 10 - 11)
March 6, 2019
geometry
Problem Statement
In the plane, let , be two closed broken lines (possibly self-intersecting), and , , , be four points. The vertices of , and the points , , are in general position (i.e. no three of these points are collinear, and no three segments between them concur at an interior point). Each of segments and meets at an even number of points, and each of segments and meets at an odd number of points. Conversely, each of segments and meets at an odd number of points, and each of segments and meets at an even number of points. Prove that and intersect.