Kamp '13 - Potencija točke 8.
Dodao/la:
arhiva3. studenoga 2013. ![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
,
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
i
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
su četiri točke na pravcu (tim redom). Kružnice nad
![|AC|](/media/m/d/5/3/d535c25714ce937c6b0e69e042f39e2f.png)
i
![|BD|](/media/m/8/4/c/84c51bd6e48f177e57d2a5361c2470a2.png)
(
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
i
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
) sijeku se u
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
i
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
. Neka je
![P \in XY](/media/m/9/f/e/9feefe75d28f03cf33fc119c2d1b7b48.png)
.
![CP \cap k_1 = M](/media/m/8/9/e/89ea234ba1dead7fba4f76358b2c8281.png)
,
![BP \cap k_2 = N](/media/m/3/b/6/3b692b72cc6fa512ee2602a0ee7731e1.png)
. Dokaži da su pravci
![AM](/media/m/9/2/1/921d54bb92ada2d2120b2591b722ea12.png)
,
![DN](/media/m/3/f/d/3fdb1985ab0a06ea4b7f886e7039b666.png)
i
![XY](/media/m/1/c/e/1ce2b6bc5783d5ee7b3276a845f41d6e.png)
konkurentni.
%V0
$A$, $B$, $C$ i $D$ su četiri točke na pravcu (tim redom). Kružnice nad $|AC|$ i $|BD|$ ($k_1$ i $k_2$) sijeku se u $X$ i $Y$. Neka je $P \in XY$. $CP \cap k_1 = M$, $BP \cap k_2 = N$. Dokaži da su pravci $AM$, $DN$ i $XY$ konkurentni.
Izvor: Kamp 2013. - Potencija točke, napredna, B. V.