Mala olimpijada 1998 zadatak 2
Dodao/la:
mljulj12. travnja 2012. Neka su
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i
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sjecišta simetrala kutova
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i
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sa stranicama trokuta
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i
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trokuta
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. Polupravac
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siječe trokutu opisanu kružnicu u točki
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. 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