Zadan je pravokutnik
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
. Simetrala dužine
![\overline{BD}](/media/m/7/3/2/732e8894e57eb20026de06c47885ae55.png)
siječe pravce
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
i
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
redom u točkama
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
i
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
. Neka su
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
polovišta dužina
![\overline{CD}](/media/m/3/3/8/338870e40f3ea7992d83158230115a5f.png)
i
![\overline{AD}](/media/m/3/0/3/303be34ac7d7fd6c29748e4abc4ee400.png)
. Dokažite da su pravci
![FM](/media/m/5/7/d/57d8386a345f7f01c20faf11567ac3d7.png)
i
![EN](/media/m/8/a/7/8a738873fd9bb9b92a40601aa803337f.png)
okomiti.
%V0
Zadan je pravokutnik $ABCD$. Simetrala dužine $\overline{BD}$ siječe pravce $AB$ i $BC$ redom u točkama $E$ i $F$. Neka su $M$ i $N$ polovišta dužina $\overline{CD}$ i $\overline{AD}$. Dokažite da su pravci $FM$ i $EN$ okomiti.