Question 6
Source: Iran TST 2006
April 30, 2006
geometryperimeterinductionabsolute valuecombinatorics proposedcombinatorics
Problem Statement
Suppose we have a simple polygon (that is it does not intersect itself, but not necessarily convex).
Show that this polygon has a diameter which is completely inside the polygon and the two arcs it creates on the polygon perimeter (the two arcs have 2 vertices in common) both have at least one third of the vertices of the polygon.