Kamp '13 - Geometrija 13.
Dodao/la:
arhiva3. studenoga 2013. Neka je
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
trokut, a
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
centar njemu opisane kružnice.
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
su redom na
![CA](/media/m/a/a/e/aaec86bc003cfdb64d54116a4cabd387.png)
i
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
. Kružnica
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
prolazi redom kroz polovišta
![BP](/media/m/e/e/f/eefb4fe46ab8d85b7067c29b24aa4cfc.png)
,
![CQ](/media/m/a/8/4/a846b659c7be23bc98305e03c8f65850.png)
i
![PQ](/media/m/f/2/f/f2f65ec376294df7eca22d2c1a189747.png)
. Pokaži da ako je
![PQ](/media/m/f/2/f/f2f65ec376294df7eca22d2c1a189747.png)
tangenta na
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
tada je
![OP = OQ](/media/m/0/d/6/0d6145d8851e1290cca2ea813bd12517.png)
.
%V0
Neka je $ABC$ trokut, a $O$ centar njemu opisane kružnice. $P$ i $Q$ su redom na $CA$ i $AB$. Kružnica $k$ prolazi redom kroz polovišta $BP$, $CQ$ i $PQ$. Pokaži da ako je $PQ$ tangenta na $k$ tada je $OP = OQ$.
Izvor: Kamp 2013. - Geometrija, M. M.