U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
simetrale kuta
![\gamma](/media/m/2/4/a/24aca7af13a8211060a900a49ef999e9.png)
pri vrhu
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
siječe nasuprotnu stranicu
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
u točki
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
. Točka
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
izvan trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
je takva da je
![|AN|=|ND|](/media/m/c/f/2/cf210b01691f87c595e6dd66c5fe9787.png)
i da je
![\angle{ADN}= \frac{\gamma}{2}](/media/m/0/6/2/0624c2deef5f21ce310d70f41a5127ae.png)
. Dokažite da je
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
simetrala kuta
![\angle{DBC}](/media/m/2/c/9/2c97782013cfce54ed12e16bb103d1e5.png)
.
%V0
U trokutu $ABC$ simetrale kuta $\gamma$ pri vrhu $C$ siječe nasuprotnu stranicu $\overline{AB}$ u točki $N$. Točka $D$ izvan trokuta $ABC$ je takva da je $|AN|=|ND|$ i da je $\angle{ADN}= \frac{\gamma}{2}$. Dokažite da je $AB$ simetrala kuta $\angle{DBC}$.