Problem

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: geometry, Equilateral Triangle



In a square with side 1 are placed $n$ equilateral triangles (without having any parts outside the square) each with side greater than $\sqrt{\frac{2}{3}}$. Prove that all of the $n$ equilateral triangles have a common inner point.