Dan je četverokut
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
. Opisana kružnica trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
siječe stranice
![\overline{CD}](/media/m/3/3/8/338870e40f3ea7992d83158230115a5f.png)
i
![\overline{DA}](/media/m/8/4/5/845d2fffb3c5eb6412b26a001c3b4b4d.png)
redom u točkama
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
, a opisana kružnica trokuta
![CDA](/media/m/d/1/9/d19754e826d51d8da2971e0b887d590c.png)
stranice
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
i
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
redom u točkama
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
i
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
. Pravci
![BP](/media/m/e/e/f/eefb4fe46ab8d85b7067c29b24aa4cfc.png)
i
![BQ](/media/m/2/8/c/28cc5d89f53243e9e0fb41492df4736b.png)
sijeku pravac
![RS](/media/m/6/5/c/65cfe2e0c3b95a4b9afb102fe26e5ef3.png)
redom u točkama
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
. Dokaži da točke
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
,
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
,
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
leže na istoj kružnici.
%V0
Dan je četverokut $ABCD$. Opisana kružnica trokuta $ABC$ siječe stranice $\overline{CD}$ i $\overline{DA}$ redom u točkama $P$ i $Q$, a opisana kružnica trokuta $CDA$ stranice $\overline{AB}$ i $\overline{BC}$ redom u točkama $R$ i $S$. Pravci $BP$ i $BQ$ sijeku pravac $RS$ redom u točkama $M$ i $N$. Dokaži da točke $M$, $N$, $P$ i $Q$ leže na istoj kružnici.