U ravnini su dane točke
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
i
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
. Neka su
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
,
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
,
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
,
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
,
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
i
![I](/media/m/3/8/6/38689d6affa9ba35368ca4d3d76ea147.png)
točke u istoj ravnini takve da su trokuti
![ABD](/media/m/a/5/4/a548bc577543629d304ecba1a042f910.png)
,
![BAE](/media/m/5/8/d/58d6e50964d732b8b39ecf6b8b6113ba.png)
,
![CAF](/media/m/1/c/0/1c095cefdead960d4773e7ea80f1b446.png)
,
![DFG](/media/m/0/9/2/0928921c61846f1071d94930f126bbe9.png)
,
![ECH](/media/m/8/6/0/860695295f3e5c999d5f6ed047f7d2c5.png)
i
![GHI](/media/m/7/2/5/725d1740b72722f3c1fd24cce7cc0dbe.png)
pozitivno orijentirani jednakostranični trokuti. Dokažite da je točka
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
polovište dužine
![\overline{AI}](/media/m/d/4/c/d4cd7675393d1ed7a96b8df6f5040634.png)
.
%V0
U ravnini su dane točke $A$, $B$ i $C$. Neka su $D$, $E$, $F$, $G$, $H$ i $I$ točke u istoj ravnini takve da su trokuti $ABD$, $BAE$, $CAF$, $DFG$, $ECH$ i $GHI$ pozitivno orijentirani jednakostranični trokuti. Dokažite da je točka $E$ polovište dužine $\overline{AI}$.