Zadan je konveksan peterokut
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
. Neka su
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
,
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
,
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
,
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
redom polovišta stranica
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
,
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
,
![\overline{CD}](/media/m/3/3/8/338870e40f3ea7992d83158230115a5f.png)
,
![\overline{DE}](/media/m/f/f/1/ff1151be8c83f905b39371ec47cb7144.png)
te neka su
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
i
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
polovišta dužina
![\overline{MP}](/media/m/2/f/9/2f9de4adf274241ff44df74b9d014344.png)
i
![\overline{QN}](/media/m/a/b/5/ab5c279092152a3a645d7c8cd1e27057.png)
. Pokažite da je
%V0
Zadan je konveksan peterokut $ABCDE$. Neka su $M$, $N$, $P$, $Q$ redom polovišta stranica $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$ te neka su $R$ i $S$ polovišta dužina $\overline{MP}$ i $\overline{QN}$. Pokažite da je $$\left\vert SR \right\vert = \frac14 \left\vert AE \right\vert \text{.}$$