Državno natjecanje 2011 SŠ2 4
Dodao/la:
arhiva1. travnja 2012. U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
vrijedi
![\left\vert AB \right\vert = \left\vert AC \right\vert](/media/m/6/7/4/674f17e6e38bc7de472c2536bef08494.png)
, a simetrala kuta
![\angle{ABC}](/media/m/6/b/9/6b9d0901c0aea1638a561ba96a7d740e.png)
siječe stranicu
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
u točki
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
tako da je
![\left\vert BC \right\vert = \left\vert BD \right\vert + \left\vert AD \right\vert](/media/m/1/2/c/12c2bf9c9a18dfe469ecb5271264851a.png)
. Odredi kutove tog trokuta.
%V0
U trokutu $ABC$ vrijedi $\left\vert AB \right\vert = \left\vert AC \right\vert$, a simetrala kuta $\angle{ABC}$ siječe stranicu $\overline{AC}$ u točki $D$ tako da je $\left\vert BC \right\vert = \left\vert BD \right\vert + \left\vert AD \right\vert$. Odredi kutove tog trokuta.
Izvor: Državno natjecanje iz matematike 2011