Marinada '24

[lang=hr] U pravokutni trokut $ABC$ s duljinom kateta $3$ i $4$, upisan je kvadrat $DEFG$ s dva susjedna vrha $D$, $E$ na hipotenuzi $\overline{AB}$ (tako da je $D$ bliže $A$) i po jednim vrhom $F$ i $G$ na katetama $\overline{BC}$ i $\overline{CA}$. Izračunajte $\left\vert AD \right\vert \cdot \left\vert BE \right\vert$. [/lang] [lang=en] In a right triangle $ABC$ with legs of lengths $3$ and $4$, a square $DEFG$ is inscribed such that two consecutive vertices $D$ and $E$ lie on the hypotenuse $\overline{AB}$ (so that $D$ is closer to $A$), and the other two vertices $F$ and $G$ lie on the legs $\overline{BC}$ and $\overline{CA}$, respectively. Calculate $\left\vert AD \right\vert \cdot \left\vert BE \right\vert$. [/lang]