Bundeswettbewerb Mathematik 1978 Problem 2.2
Source: Bundeswettbewerb Mathematik 1978 Round 2
October 21, 2022
geometrysquareareaVerticesTriangle
Problem Statement
Seven distinct points are given inside a square with side length Together with the square's vertices, they form a set of points. Consider all triangles with vertices in a) Show that at least one of these triangles has an area not exceeding 1\slash 16.b) Give an example in which no four of the seven points are on a line and none of the considered triangles has an area of less than 1\slash 16.