Given a triangle ABC with an interior point P and points Q1,Q2 not lying on any of the segments AB,AC,BC, AP,BP,CP, show that there does not exist a polygonal line K joining Q1 and Q2 such that
i) K crosses each segment exactly once,
ii) K does not intersect itself
iii) K does not pass through A,B,C or P. Putnamgeometrypolygonlines