Županijsko natjecanje iz matematike 2015, SŠ2 A 4
Dodao/la:
arhiva22. ožujka 2015. Neka je

središte opisane kružnice, a

ortocentar trokuta

. Pravac

siječe opisanu kružnicu u točki

. Dokaži da pravac

prolazi polovištem stranice

.
%V0
Neka je $O$ središte opisane kružnice, a $H$ ortocentar trokuta $ABC$. Pravac $AO$ siječe opisanu kružnicu u točki $D$. Dokaži da pravac $HD$ prolazi polovištem stranice $\overline{BC}$.
Izvor: Županijsko natjecanje iz matematike 2015