Neka je
trokut u kome je
,
. Njemu upisana kružnica dodiruje
u
redom. Neka je
nožište visine iz
na
. Ako je
nađi
. Rješenje zaokruži na
decimale.
Let
be a triangle in which
,
. The circle inscribed to it touches
in
respectively. Let
be the base of the height from
to
. If
find
. Round the solution to
decimal places.
[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]