U tetivnom četverokutu
,
.
siječe
u
. Pravac
siječe dužine
u
redom. Ako
i
. Neka je
centar opisane kružnice
izračunaj
.
In a cyclic quadrilateral
,
. Let
intersect
at
. Line
intersects segments
at
respectively. Assume that
and
. Finally, let
be the circumcenter of
. Evaluate
.
[lang=hr]
U tetivnom četverokutu $ABCD$, $\angle A+ \angle D=\frac{\pi}{2}$. $AC$ siječe $BD$ u ${E}$. Pravac ${l}$ siječe dužine $AB, CD, AE, DE$ u $X, Y, Z, T$ redom. Ako $AZ=CE$ i $BE=DT$. Neka je $O$ centar opisane kružnice $\triangle EZT$ izračunaj $\frac{OE}{XY}$.
[/lang]
[lang=en]
In a cyclic quadrilateral $ABCD$, $\angle A+ \angle D=\frac{\pi}{2}$. Let $AC$ intersect $BD$ at ${E}$. Line ${l}$ intersects segments $AB, CD, AE, DE$ at $X, Y, Z, T$ respectively. Assume that $AZ=CE$ and $BE=DT$. Finally, let $O$ be the circumcenter of $\triangle EZT$. Evaluate $\frac{OE}{XY}$.
[/lang]
