Five points lie inside an equilateral triangle of side 2 units.Prove that at least 2 points are no more than a unit distance apart.
2026-03-29 20:45:45.1774817145
Least distance between two points in an equilateral triangle
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Connect the midpoints of the sides to each other. This divides the original triangle into four smaller, congruent equilateral triangles of side 1 unit. You have five points and only four triangles, so two points must be in one of the triangles. They can't be more than one unit apart.