U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
su dane visine
![\overline{AA_1}](/media/m/c/e/0/ce0f593d6c26e68e43cdec387679a569.png)
,
![\overline{BB_1}](/media/m/0/0/b/00b72a523b335829db073b0e23cccda7.png)
,
![\overline{CC_1}](/media/m/d/b/4/db42ab8506d35c0ef8f5d16e6448d537.png)
, pri čemu je
![\overrightarrow{AA_1} + \overrightarrow{BB_1} + \overrightarrow{CC_1} = \overrightarrow{0}\text{.}](/media/m/d/c/e/dcec90afaae96a19367d595e5698560b.png)
Dokažite da je trokut
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
jednakostraničan.
%V0
U trokutu $ABC$ su dane visine $\overline{AA_1}$, $\overline{BB_1}$, $\overline{CC_1}$, pri čemu je $$\overrightarrow{AA_1} + \overrightarrow{BB_1} + \overrightarrow{CC_1} = \overrightarrow{0}\text{.}$$
Dokažite da je trokut $ABC$ jednakostraničan.