Zadatak je iz tangente broj 64/4 godina 2010/2011,strana 43(Geometrija za Matematicku gimnaziju),5.zadatak.
U unutrasnjosti trougla
![](https://static.elitesecurity.org/tex/1ab583dfcab2387f05241f03445f082c.png)
tacke
![](https://static.elitesecurity.org/tex/fd67595d361d6b4b243b65ed68634716.png)
su podnozja visina iz temena
![](https://static.elitesecurity.org/tex/49154cdda39f5afd07317aab320f43dc.png)
,a tacka
![](https://static.elitesecurity.org/tex/606d929fde93928da33e62372f271e40.png)
ortocentar.Dokazi da vazi:
![](https://static.elitesecurity.org/tex/fb337477651723e201e71ebac9868063.png)
.
Evo kako sam ja poceo:
![](https://static.elitesecurity.org/tex/0624ccfdc2c6483e9889c1e84df5ca7d.png)
i
![](https://static.elitesecurity.org/tex/072a2ddfa1219bc72a0dccf3829582ea.png)
i
![](https://static.elitesecurity.org/tex/3cbb719be765ad7320e260f006884bc4.png)
i
![](https://static.elitesecurity.org/tex/dc4dafda3e60d12e23877cf33f47e9a0.png)
,
Dalje se dobija konacna jednakost:
![](https://static.elitesecurity.org/tex/6afd39c6110a0b5632459192f8ca4fcd.png)
,tj. ako stavimo da je
![](https://static.elitesecurity.org/tex/8c96cd8c5131368dc8bb0185417164a3.png)
:
![](https://static.elitesecurity.org/tex/42efd38bc925527d1dd12d60f34f2ddf.png)
.
Dalje sam mislio da nekako izrazim
![](https://static.elitesecurity.org/tex/1dcbe90e6f7c03f5fbf137ce83f8335e.png)
i
![](https://static.elitesecurity.org/tex/4b2facd962041490f51cf7685d3ad44b.png)
,Ima li ko ideju kako da nastavim?
حياتي هو العلم بلدي (الرياضيات)