Marinada '23

[lang=hr] Dan je romb $ABCD$ i točka $P$ na stranici $BC$: Neka je $E$ presjek pravca $AD$ i okomice iz točke $P$ na $DB$, a $F$ presjek pravca $AD$ i okomice iz točke $P$ na $AC$. Pretpostavimo da se pravci $BE, AP$ i $CF$ sjeku u jednoj točci. Koliki je omjer duljina dužina $BP$ i $PC$? [/lang] [lang=en] Rhombus $ABCD$ and a point $P$ on the side $BC$ are given: Let $E$ be the intersection of the line $AD$ and the perpendicular from the point $P$ to $DB$, and let $F$ be the intersection of the line $AD$ and the perpendicular from point $P$ to $AC$. Suppose that the lines $BE, AP$ and $CF$ intersect at one point. What is the ratio of the lengths of $BP$ and $PC$? [/lang]