Neka je
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
središte opisane kružnice, a
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
ortocentar trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Pravac
![AO](/media/m/d/9/3/d93e4e1fde6437bd5210d0a50abb3ca8.png)
siječe opisanu kružnicu u točki
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
. Dokaži da pravac
![HD](/media/m/5/1/4/5146e5f91d5bcf75e040663d047ba717.png)
prolazi polovištem stranice
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
.
%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 $\overline{BC}$.