MathNet 2019-part-05 — 184 problems (EN–VI) Question 58

Let $a, b, c$ be distinct complex numbers, such that $|a| = |b| = |c| = 1$. Prove that if $|a+b-c|^2 + |b+c-a|^2 + |c+a-b|^2 = 12$, then the geometric images of $a, b, c$ are the vertices of an equilateral triangle.
Mihaela Berindeanu