OMCPLP 2024 Problem 4

Day 2

Na figura, os triângulos $ABC$ e $CDE$ são equiláteros, de lados 1 e 4, respetivamente. Além disso, $B$ , $C$ e $D$ são colineares e $F$ e $G$ são os pontos médios de $BC$ e $CD$ , respetivamente. Seja $P$ o ponto de interseção de $AF$ com $BE$ . Determine a área do triângulo sombreado $BPG$ .

Official text Lusophon Mathematical Olympiad 2024 official paper, page 2. Quoted with source.

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