Neka se točke
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
i
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
nalaze redom na stranicama
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
i
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Simetrale kutova
![\angle ABE](/media/m/a/4/3/a43dc611b7a5362c55de2ded4dc386db.png)
i
![\angle ACD](/media/m/6/7/9/679c6f2efbcacfd6fdbe7d626316ecde.png)
sijeku se u točki
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
. Dokažite da je
![\angle BDC + \angle BEC = 2 \angle BFC](/media/m/4/e/8/4e8bc0a49edf1c35387dbd8bae31d565.png)
.
%V0
Neka se točke $D$ i $E$ nalaze redom na stranicama $AB$ i $AC$ trokuta $ABC$. Simetrale kutova $\angle ABE$ i $\angle ACD$ sijeku se u točki $F$. Dokažite da je $\angle BDC + \angle BEC = 2 \angle BFC$.