If $AG_a,BG_b$, and $CG_c$ are symmedians in $\Delta ABC$ ($G_a\in BC,G_b\in AC,G_c\in AB$), is it possible for $\Delta G_a G_b G_c$ to be equilateral when $\Delta ABC$ is not equilateral?
Problem
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: geometry, Symmedians, Equilateral Triangle