Mala olimpijada 1998 zadatak 2
Dodao/la:
mljulj12. travnja 2012. Neka su
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
sjecišta simetrala kutova
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
i
![\angle ACB](/media/m/2/b/8/2b827c330f4f220b112b928e106c0a00.png)
sa stranicama trokuta
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
i
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Polupravac
![MN](/media/m/2/6/7/267a73297a5de9e529d41774ee6ff45a.png)
siječe trokutu opisanu kružnicu u točki
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
. Dokažite da je
%V0
Neka su $M$ i $N$ sjecišta simetrala kutova $\angle ABC$ i $\angle ACB$ sa stranicama trokuta $\overline{AC}$ i $\overline{AB}$ trokuta $ABC$. Polupravac $MN$ siječe trokutu opisanu kružnicu u točki $D$. Dokažite da je
$$ \frac{1}{|BD|} = \frac{1}{|AD|}+ \frac{1}{|CD|} .$$
Izvor: Mala olimpijada 1998 zadatak 2