Ćevidova lema. Neka se dvije kružnice
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
,
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
sijeku u točkama
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
. Neka su na
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
odabrane dvije točke
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
,
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
. Neka tangenta iz
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
dira
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
u
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
, tangenta iz
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
dira
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
u
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
, tangenta iz
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
dira
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
u
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
, te tangenta iz
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
dira
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
u
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
. Također, neka su sve tangente s iste strane pravca
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
. Dokaži da je
![KLMN](/media/m/5/9/0/5906903433d8aca833f74f8c34b46b24.png)
tetivan.
%V0
Ćevidova lema. Neka se dvije kružnice $k_1$, $k_2$ sijeku u točkama $A$, $B$. Neka su na $AB$ odabrane dvije točke $X$, $Y$. Neka tangenta iz $X$ dira $k_1$ u $K$, tangenta iz $X$ dira $k_2$ u $L$, tangenta iz $Y$ dira $k_1$ u $M$, te tangenta iz $Y$ dira $k_2$ u $N$. Također, neka su sve tangente s iste strane pravca $AB$. Dokaži da je $KLMN$ tetivan.