Visina
![\overline{CD}](/media/m/3/3/8/338870e40f3ea7992d83158230115a5f.png)
na hipotenuzu
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
pravokutnog trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
je promjer kružnice
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
koja siječe katete
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
i
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
tog trokuta redom u točkama
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
i
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
. Ako je
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
sjecište pravaca
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
i
![EF](/media/m/f/5/5/f5594d5ec47ea777267cf010e788fedd.png)
i ako vrijedi
![|CG|^2=|CE|\cdot|CF|,](/media/m/e/3/4/e344a89d59b5d2ccf067daaa364935e1.png)
koliki su šiljasti kutovi trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
?
%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 $ABC$?