Kamp '13 - Geometrija 5.
Dodao/la:
arhiva3. studenoga 2013. Dvije kružnice
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
,
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
sijeku se u
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
. Neka je
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
točka na
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
, a
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
na
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
takva da su
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
,
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
i
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
kolinearne. Dokažite da omjer
![|BP|/|BQ|](/media/m/6/2/f/62fe44a20ba807de7f8d938258fdabce.png)
ne ovisi o odabiru točaka
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
.
%V0
Dvije kružnice $k_1$, $k_2$ sijeku se u $A$, $B$. Neka je $P$ točka na $k_1$, a $Q$ na $k_2$ takva da su $P$, $Q$ i $A$ kolinearne. Dokažite da omjer $|BP|/|BQ|$ ne ovisi o odabiru točaka $P$ i $Q$.
Izvor: Kamp 2013. - Geometrija, M. M.