IGO 2020 E3

Elementary

According to the figure, three equilateral triangles with side lengths $a,b,c$ have one common vertex and do not have any other common point. The lengths $x, y$ , and $z$ are defined as in the figure. Prove that $3(x+y+z)>2(a+b+c)$ . Proposed by Mahdi Etesamifard

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Dataset text AI-MO AoPS. Quoted with source.

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