3 points out of 4 in a convex ABCD of area 1 with area >=1/4
Source: 1992 ITAMO p2
January 31, 2020
geometryareacombinatorial geometryarea of a trianglearea of triangle
Problem Statement
A convex quadrilateral of area is given. Prove that there exist four points in the interior or on the sides of the quadrilateral such that each triangle with the vertices in three of these four points has an area greater than or equal to .