Marinada '25

[lang=hr] U trokutu $ABC$, $D$,$E$ i $F$ su polovišta stranica $\overline{AC}$, $\overline{BC}$ i $\overline{AB}$, tim redom. Kružnica opisana trokutu $CDE$ prolazi težištem trokuta $ABC$. Odredi vrijednost izraza $$\frac{|CF|}{|AB|}.$$ [/lang] [lang=en] In triangle $ABC$, $D$, $E$, and $F$ are the midpoints of sides $\overline{AC}$, $\overline{BC}$, and $\overline{AB}$, respectively. The circumcircle of triangle $CDE$ passes through the centroid of triangle $ABC$. Determine the value of the expression $$ \frac{|CF|}{|AB|} .$$ [/lang]