Question 35
Let's call the intersection of two segments *almost perfect* if for each of them the length of the segment is at least $2021$ times the distance between its midpoint and the intersection point.
Prove that there exists a closed broken line that intersects each of its segments at least once and for which all its intersections are almost perfect.
Prove that there exists a closed broken line that intersects each of its segments at least once and for which all its intersections are almost perfect.