Five points are arbitrarily put inside a given equilateral triangle ABC whose area is equal to 1. Show that we can draw three equilateral triangles within triangle ABC 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 ABC;
iii) the sum of the areas of the three equilateral triangles is not larger than 0.64. geometrygeometry unsolved