Županijsko natjecanje 1996 SŠ3 2
Dodao/la:
arhiva1. travnja 2012. Na stranici
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
leže redom točke
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
,
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
i
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
, pri čemu je
![\overline{AN}](/media/m/1/f/0/1f0b39eab6c0ee75e00e935cbb0f1801.png)
visina,
![AL](/media/m/4/b/f/4bf7fa7e437910d053f4fbe634746a58.png)
simetrala kuta
![\angle CAB](/media/m/4/c/8/4c8433a2baf2fc63fcfcfd6b2715c08b.png)
i
![\overline{AM}](/media/m/8/4/2/842c50b06828638f5987f7dd1ed963a6.png)
težišnica. Ako je
![\angle NAB=\angle LAN=\angle MAL=\angle CAM](/media/m/4/7/f/47f192f49b8b3b853502fa894a8fb9b5.png)
, odredite kutove trokuta.
%V0
Na stranici $\overline{BC}$ trokuta $ABC$ leže redom točke $N$, $L$ i $M$, pri čemu je $\overline{AN}$ visina, $AL$ simetrala kuta $\angle CAB$ i $\overline{AM}$ težišnica. Ako je $\angle NAB=\angle LAN=\angle MAL=\angle CAM$, odredite kutove trokuta.
Izvor: Županijsko natjecanje iz matematike 1996