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Similar to BMO SL 2022 A6

Source: 2023 Macedonian Team Selection Test P4

May 21, 2023
geometry

Problem Statement

Let f:R2→Rf: \mathbb{R}^2 \to \mathbb{R} be a function satisfying the following property: If A,B,C∈R2A, B, C \in \mathbb{R}^2 are the vertices of an equilateral triangle with sides of length 11, then f(A)+f(B)+f(C)=0.f(A) + f(B) + f(C) = 0. Show that f(x)=0f(x) = 0 for all x∈R2x \in \mathbb{R}^2.
Proposed by Ilir Snopce
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