Državno natjecanje 2006 SŠ2 3
Kvaliteta:
Avg: 0,0Težina:
Avg: 4,0 Kružnice
i
sijeku se u točkama
i
. Tangenta kružnice
povučena iz točke
siječe kružnicu
u točki
, a tangenta kružnice
povučena iz točke
siječe kružnicu
u točki
. Polupravac kroz točku
, koji leži unutar kuta
, siječe kružnicu
u točki
, kružnicu
u točki
i kružnicu opisanu trokutu
u točki
. Dokaži da je udaljenost točaka
i
jednaka udaljenosti točaka
i
.
![C_1](/media/m/b/0/b/b0b10dc32c3e01824e0f0b6753ac2537.png)
![C_2](/media/m/a/b/8/ab898e857261e1c35339f3f3d8362ba0.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![C_2](/media/m/a/b/8/ab898e857261e1c35339f3f3d8362ba0.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![C_1](/media/m/b/0/b/b0b10dc32c3e01824e0f0b6753ac2537.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![C_1](/media/m/b/0/b/b0b10dc32c3e01824e0f0b6753ac2537.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![C_2](/media/m/a/b/8/ab898e857261e1c35339f3f3d8362ba0.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![\angle{CAD}](/media/m/f/b/c/fbc5ea172622c1d4d8f779d691e8b8e0.png)
![C_1](/media/m/b/0/b/b0b10dc32c3e01824e0f0b6753ac2537.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![C_2](/media/m/a/b/8/ab898e857261e1c35339f3f3d8362ba0.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![ACD](/media/m/0/b/1/0b171034d79122bd02f64bc8f6ae94dd.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
Izvor: Državno natjecanje iz matematike 2006