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2020 IGO Elementary P3

Source: 7th Iranian Geometry Olympiad (Elementary) P3

November 4, 2020
geometryIGO

Problem Statement

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