Općinsko natjecanje 2003 SŠ2 2
Dodao/la:
arhiva2. travnja 2012. U jednakostraničnom trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
dane su točke
![D\in \overline{AB}](/media/m/8/9/4/894522a49a361e59de584c861683c74d.png)
i
![E\in \overline{BC}](/media/m/a/e/0/ae0ad290eb48ba3c38028b8d99c1dba9.png)
takve da je
![|AD|=\displaystyle\dfrac{1}{3}|AB|](/media/m/5/0/d/50d4e8ce32c67e476de9362ad236cd4d.png)
i
![|BE|=\displaystyle\dfrac{1}{3}|BC|](/media/m/2/8/4/284f5e8ae51e7937bde508c648782630.png)
. Pravci
![AE](/media/m/c/e/3/ce31f42a92358c211bccb23e6a92fb55.png)
i
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
sijeku se u točki
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
. Koliki je kut
![\angle BPC](/media/m/b/9/d/b9d947ed7773fec87c2f98aa0fd8e8a8.png)
?
%V0
U jednakostraničnom trokutu $ABC$ dane su točke $D\in \overline{AB}$ i $E\in \overline{BC}$ takve da je $|AD|=\displaystyle\dfrac{1}{3}|AB|$ i $|BE|=\displaystyle\dfrac{1}{3}|BC|$. Pravci $AE$ i $CD$ sijeku se u točki $P$. Koliki je kut $\angle BPC$?
Izvor: Općinsko natjecanje iz matematike 2003