Unutar trokuta ABCABCABC s duljinama stranica a,b,ca, b, ca,b,c i odgovarajućim kutovima α,β,γ\alpha, \beta, \gammaα,β,γ postoje točke PPP i QQQ takve da vrijedi ∡BPC=∡CPA=∡APB=120°,\measuredangle BPC = \measuredangle CPA = \measuredangle APB = 120°,∡BPC=∡CPA=∡APB=120°, ∡BQC=60°+α,∡CQA=60°+β,∡AQB=60°+γ.\measuredangle BQC = 60° + \alpha, \quad \measuredangle CQA = 60° + \beta, \quad \measuredangle AQB = 60° + \gamma.∡BQC=60°+α,∡CQA=60°+β,∡AQB=60°+γ.
Dokažite da vrijedi jednakost (∣AP∣+∣BP∣+∣CP∣)3⋅∣AQ∣⋅∣BQ∣⋅∣CQ∣=(abc)2.(|AP| + |BP| + |CP|)^3 \cdot |AQ| \cdot |BQ| \cdot |CQ| = (abc)^2.(∣AP∣+∣BP∣+∣CP∣)3⋅∣AQ∣⋅∣BQ∣⋅∣CQ∣=(abc)2.