Marinada '23

[lang=hr] Neka su točke $P$ i $Q$, redom na stranicama $BC$ i $CA$ trokuta $ABC$, takve da važi $BC:PC=6:1$, $CQ : AC = 3 : 13$. Neka je $E$ sjecište pravaca $AP$ i $BQ$, a $R$ sjecište pravaca $CE$ i $AB$. Nađi: \begin{center} $\frac{AR}{RB}+\frac{AE}{EP}$ \end{center} Odgovor zaokruži na dvije decimale. [/lang] [lang=en] Choose points $P$ and $Q$ on sides $BC$ and $CA$ of the triangle $ABC$ respectively, such that $BC:PC=6:1$, $CQ : AC = 3 : 13$. Let $E$ be the intersection of lines $AP$ and $BQ$, and $R$ intersection of lines $CE$ and $AB$. Find \begin{center} $\frac{AR}{RB}+\frac{AE}{EP}$ \end{center}. Round your answer to two decimal places. [/lang]