géométrie lycée recueilchapitre 4exercice 4.7vecteurs

A relation between medians

Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · ★★★★★

Statement

Dans un triangle $ABC$, soient $AD$ et $BE$ deux médianes, se coupant en $G$. Montrez que \[ AB^2 + BC^2 + CA^2 = 3(GD^2 + GE^2) + \frac{3}{4}(AB^2 + BC^2 + CA^2). \]

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Origin : Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar

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