Marinada '23

[lang = hr] Neka je $ABCD$ tetivni četverokut u kome je $AB < BC$ i $AD < DC$. Neka su $X$ i $Y$ točke na stranicama $BC$ i $CD$, redom, takve da vrijedi $AB = BX$ i $AD = DY$. Neka je $S$ polovište dužine $XY$. Odredi $\angle BSD$. Rješenje zaokruži na 2 decimale. [/lang] [lang = en] Let $ABCD$ be a cyclic quadrilateral in which $AB < BC$ and $AD < DC$. Let $X$ and $Y$ be points on sides $BC$ and $CD$, respectively, such that $AB = BX$ and $AD = DY$ hold. Let $S$ be half the length of $XY$. Determine $\angle BSD$. Round the solution to 2 decimal places. [/lang]