Županijsko natjecanje 1997 SŠ3 2
Dodao/la:
arhiva1. travnja 2012. U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
povučene su simetrale
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
i
![BE](/media/m/e/e/2/ee25cd134664bc0c8d7fdbba81e54f90.png)
kutova
![\angle CAB](/media/m/4/c/8/4c8433a2baf2fc63fcfcfd6b2715c08b.png)
i
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
(
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
i
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
su točke na stranicama
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
i
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
). Nađite kut
![\gamma = \;\angle BCA](/media/m/3/4/7/347ec99535cadd900669b23f88af7e90.png)
ako je
![|AD|\cdot |BC| = |BE|\cdot |AC|\;](/media/m/2/8/7/287e94d30be2d625d6c3769d6111548b.png)
i
%V0
U trokutu $ABC$ povučene su simetrale $AD$ i $BE$ kutova $\angle CAB$ i $\angle ABC$ ($D$ i $E$ su točke na stranicama $\overline{BC}$ i $\overline{AC}$). Nađite kut $\gamma = \;\angle BCA$ ako je $|AD|\cdot |BC| = |BE|\cdot |AC|\;$ i $\;|AC|\ne |BC|.$
Izvor: Županijsko natjecanje iz matematike 1997