Unexpectedly difficult combo geo
Source: Mongolian Mathematical Olympiad 2024 P2
April 12, 2024
combinatoricsgeometryExtremal
Problem Statement
We call a triangle consisting of three vertices of a pentagon big if it's area is larger than half of the pentagon's area. Find the maximum number of big triangles that can be in a convex pentagon.Proposed by Gonchigdorj Sandag