Općinsko natjecanje 1996 SŠ2 4
Dodao/la:
arhiva2. travnja 2012. U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
poznate su duljine stranica
![b=|AC|](/media/m/5/1/9/5191baa407f0ac68053cdfe88eceae82.png)
i
![c=|AB|](/media/m/d/b/a/dba5858c55f4f26bb5910b6d34e63b1a.png)
i
![\angle ABC=3\angle BCA.](/media/m/5/9/f/59f8c7fe8cd37aaecdc404862e06bd1c.png)
Na stranici
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
odabrane su točke
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
i
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
takve da je
![\angle ABD=\angle DBE=\angle EBC.](/media/m/8/8/5/88512affb240e25c0ee09a3d6f0bc96d.png)
Izrazite pomoću
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
i
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
duljine dužina
![\overline{DE}](/media/m/f/f/1/ff1151be8c83f905b39371ec47cb7144.png)
i
![\overline{EC}](/media/m/5/b/b/5bb4f62da6c45de0eaf91964064f3c64.png)
.
%V0
U trokutu $ABC$ poznate su duljine stranica $b=|AC|$ i $c=|AB|$ i $\angle ABC=3\angle BCA.$ Na stranici $\overline{AC}$ odabrane su točke $D$ i $E$ takve da je $\angle ABD=\angle DBE=\angle EBC.$ Izrazite pomoću $b$ i $c$ duljine dužina $\overline{AD},$ $\overline{DE}$ i $\overline{EC}$.
Izvor: Općinsko natjecanje iz matematike 1996