Marinada '24

[lang=hr] Zadan je trokut $ABC$. Neka su $D$ i $E$ točke na stranici $BC$ takve da vrijedi $BD=DE=EC$. Neka je $F$ polovište stranice $AC$. Pravac $BF$ siječe $AD$ u točki $P$, a $AE$ u točki $Q$. Odredite omjer površine trokuta $APQ$ i četverokuta $PDEQ$. Napišite odgovor u obliku razlomka poput $a/b$. [/lang] [lang=en] Let $ABC$ be a triangle. Let $D,E$ be points on the segment $BC$ such that $BD=DE=EC$. Let $F$ be the mid-point of $AC$. Let $BF$ intersect $AD$ in $P$ and $AE$ in $Q$ respectively. Determine the ratio of the area of the triangle $APQ$ to that of the quadrilateral $PDEQ$. Write the answer in fraction form like a/b. [/lang]