En el triangle ABC , el punt E divideix el costat BC, de tal manera que [math]\frac{BE}{EC}=2[/math]. El punt D fa que l'àrea del triangle BED sigui la meitat de l'àrea del triangle ABC. Quina relació hi ha entre les longituds de BD i de DA?[br][br][img 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[/img]