China Mathematical Olympiad 1987 problem4
Source: China Mathematical Olympiad 1987 problem4
January 9, 2014
geometrygeometry unsolved
Problem Statement
Five points are arbitrarily put inside a given equilateral triangle whose area is equal to . Show that we can draw three equilateral triangles within triangle such that the following conditions are all satisfied:
i) the five points are covered by the three equilateral triangles;
ii) any side of the three equilateral triangles is parallel to a certain side of the triangle ;
iii) the sum of the areas of the three equilateral triangles is not larger than .