Iranian Geometry Olympiad 2020 (Elementary) P3
Posted: Sat Dec 12, 2020 4:59 pm
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 $3(x + y + z) \gt 2(a + b + c)$.