Dijagonale tetivnog četverokuta
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
sijeku se u
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
. Kružnica opisana trokutu
![ABS](/media/m/1/0/8/108bd23ed91cf3cbec7a9de9dc5e498b.png)
siječe pravac
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
u točki
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
, a kružnica opisana trokutu
![ADS](/media/m/4/4/f/44f21e0a76118062dee33e9d6b84d293.png)
siječe pravac
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
u točki
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
. Dokažite da su
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
,
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
,
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
kolinearne.
%V0
Dijagonale tetivnog četverokuta $ABCD$ sijeku se u $S$. Kružnica opisana trokutu $ABS$ siječe pravac $BC$ u točki $M$, a kružnica opisana trokutu $ADS$ siječe pravac $CD$ u točki $N$. Dokažite da su $S$, $M$, $N$ kolinearne.