Marinada '24

[lang=hr] Neka je $ABC$ trokut u kome je $AB=20$, $AC=22$. Njemu upisana kružnica dodiruje $BC,CA,AB$ u $X,Y,Z$ redom. Neka je $D$ nožište visine iz $X$ na $YZ$. Ako je $\angle BDC=90^{\circ}$ nađi $BC$. Rješenje zaokruži na $3$ decimale. [/lang] [lang=en] Let $ABC$ be a triangle in which $AB=20$, $AC=22$. The circle inscribed to it touches $BC,CA,AB$ in $X,Y,Z$ respectively. Let $D$ be the base of the height from $X$ to $YZ$. If $\angle BDC=90^{\circ}$ find $BC$. Round the solution to $3$ decimal places. [/lang]