Županijsko natjecanje 1998 SŠ1 3
Dodao/la:
arhiva1. travnja 2012. Visina
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na hipotenuzu
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pravokutnog trokuta
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je promjer kružnice
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koja siječe katete

i

tog trokuta redom u točkama
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i
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. Ako je
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sjecište pravaca
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i
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i ako vrijedi

koliki su šiljasti kutovi trokuta

?
%V0
Visina $\overline{CD}$ na hipotenuzu $\overline{AB}$ pravokutnog trokuta $ABC$ je promjer kružnice $k$ koja siječe katete $\overline{AC}$ i $\overline{BC}$ tog trokuta redom u točkama $E$ i $F$. Ako je $G$ sjecište pravaca $CD$ i $EF$ i ako vrijedi $$
|CG|^2=|CE|\cdot|CF|,
$$ koliki su šiljasti kutovi trokuta $ABC$?
Izvor: Županijsko natjecanje iz matematike 1998