skakavac 2014 prvo kolo ss3 3
Kvaliteta:
Avg: 0,0Težina:
Avg: 4,0 Zadane su 2 kružnice,
i
, koje se sijeku u točkama
i
. Neka je
pravac određen točkama
i
. Dane su proizvoljne točke
i
s pravca
tako da je dužina
sadržana u dužini
, te tako da vrijedi
. Na kružnici
, odabrane su točke
i
, s iste strane pravca
, takve da su pravci
i
tangente na kružnicu
. Na kružnici
, odabrane su točke
i
, s iste strane pravca
, ali s različite strane u odnosu na točke
i
, takve da su pravci
i
tangente na kružnicu
. Dokažite da se pravci
i
sijeku u točki koja je na pravcu
.
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![l](/media/m/e/e/9/ee975101080f37986f56baaf4c3cdcd2.png)
![A_1](/media/m/5/a/6/5a6ce1347567551c02239ff8d4ebee67.png)
![B_1](/media/m/5/d/9/5d9518a7c0ead344571aac61b51bb25c.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![A_1](/media/m/5/a/6/5a6ce1347567551c02239ff8d4ebee67.png)
![B_1](/media/m/5/d/9/5d9518a7c0ead344571aac61b51bb25c.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![\overline{A_1B_1}](/media/m/d/c/2/dc2bd6d9f5e72c0dd287663943db62f3.png)
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
![0 \neq |AA_1| \neq |BB_1| \neq 0](/media/m/0/c/8/0c83df7c2d4943e9fb46cd5984debc5c.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![AM](/media/m/9/2/1/921d54bb92ada2d2120b2591b722ea12.png)
![BN](/media/m/9/2/3/923313310d49dd4405c2a3573960a679.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![l](/media/m/e/e/9/ee975101080f37986f56baaf4c3cdcd2.png)
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![AR](/media/m/f/3/5/f357f08b4fdbd7fe7522df290756074f.png)
![BS](/media/m/3/0/f/30f1debf47f15e4cdb55f1f18a034c23.png)
![l](/media/m/e/e/9/ee975101080f37986f56baaf4c3cdcd2.png)
![MN](/media/m/2/6/7/267a73297a5de9e529d41774ee6ff45a.png)
![RS](/media/m/6/5/c/65cfe2e0c3b95a4b9afb102fe26e5ef3.png)
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
Izvor: skakavac