Županijsko natjecanje 2011 SŠ4 4
Kvaliteta:
Avg: 0,0Težina:
Avg: 4,0 Kružnice
i
, polumjera
i
redom (
) dodiruju se iznutra u točki
. Neka je
pravac paralelan njihovoj zajedničkoj tangenti, neka je
jedno sjecište pravca
s kružnicom
, a
jedno sjecište pravca
s kružnicom
, tako da se točke
i
nalaze s iste strane pravca koji spaja središta danih kružnica. Dokaži da polumjer kružnice opisane trokutu
ne ovisi o izboru pravca
i izrazi taj polumjer pomoću
i
.
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
![r<R](/media/m/5/1/7/51750099be09090c030631cc31f71eba.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
Izvor: Županijsko natjecanje iz matematike 2011