Općinsko natjecanje 1995 SŠ1 1
Dodao/la:
arhiva2. travnja 2012. Na stranici
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
leže točke
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
,
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
,
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
tako da je
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
između
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
i
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
, a
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
između
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
i
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
. Ako je
![|BH| = |BC|](/media/m/6/2/3/623e324ff774af2d4041eac587040090.png)
,
![|HG| = |HC|](/media/m/c/d/3/cd3466f1985a795a2bd8c64f1335eec6.png)
,
![|GF| = |GC|](/media/m/5/8/2/582293d6a2f2446d1a4e08aa26809b06.png)
,
![|FA| = |FC|](/media/m/7/e/a/7ead2adcc0d2d41bee361e3808de8f0c.png)
, te
![\angle {CAB} = 5^{\circ}](/media/m/d/4/b/d4b0a0931eab8e8ca30864f733785223.png)
, izračunajte koliki je
![\angle {ABC}](/media/m/c/0/b/c0bbb43ec6fcc5799445e8066cdbf051.png)
.
%V0
Na stranici $\overline{AB}$ trokuta $ABC$ leže točke $F$, $G$, $H$ tako da je $F$ između $A$ i $G$, a $H$ između $G$ i $B$. Ako je $|BH| = |BC|$, $|HG| = |HC|$, $|GF| = |GC|$, $|FA| = |FC|$, te $\angle {CAB} = 5^{\circ}$, izračunajte koliki je $\angle {ABC}$.
Izvor: Općinsko natjecanje iz matematike 1995