Marinada '23

[lang=hr] Dan je jednakokračan $\triangle ABC$ s osnovicom $BC$ duljine $20$ i krakovima duljine $21$. Točke $D, E$ su redom na stranicama $AB, AC$ takve da je dužina $DE$ paralelna osnovici. Točka $F$ se nalazi unutar $\triangle ABC$ tako da je četverokut $ADFE$ tetivan i vrijedi $DF=3, FE=4$. Omjer površina četverokuta $ADFE$ i $\triangle ABC$ se može izraziti kao razlomak $\frac{a}{b}$, gdje su $a$ i $b$ relativno prosti prirodni brojevi. Koliko je $a+b$? [/lang] [lang=en] An isosceles $\triangle ABC$ with a base $BC$ of length $20$ and legs of length $21$ is given. The points $D, E$ are respectively on the sides $AB, AC$ such that the $DE$ is parallel to the base. Point $F$ is inside $\triangle ABC$ so that quadrilateral $ADFE$ is cyclic and $DF=3, FE=4$ holds. The ratio of the areas of quadrilateral $ADFE$ and $\triangle ABC$ can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. What is the value of $a+b$? [/lang]