Dane su točke
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
i
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
, dok je
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
varijabilna, takva da je
![\angle BAC](/media/m/b/2/1/b21a9e466104c5d33646432221e142be.png)
fiksan. Polovišta stranica
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
i
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
su točke
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
i
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
redom. Točke
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
i
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
su takve da je
![DF \perp AB](/media/m/e/7/8/e78f9fa24d7eb5b54c730de19802b3dc.png)
i
![EG \perp AC](/media/m/3/d/c/3dc8185f0f21cd8cef06f80d50d5fb76.png)
, a
![BF](/media/m/4/d/4/4d4fbb8bdcff87c5df52488beb896501.png)
i
![CG](/media/m/a/b/7/ab73fca8f0d6d8f7deac651e6a181c98.png)
su okomite na
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
. Dokažite da umnožak
![|BF| \cdot |CG|](/media/m/2/0/c/20c6c39b801c7d7cafda9fc009abdf3d.png)
ne ovisi o položaju točke
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
.
%V0
Dane su točke $B$ i $C$, dok je $A$ varijabilna, takva da je $\angle BAC$ fiksan. Polovišta stranica $\overline{AB}$ i $\overline{AC}$ su točke $D$ i $E$ redom. Točke $F$ i $G$ su takve da je $DF \perp AB$ i $EG \perp AC$, a $BF$ i $CG$ su okomite na $BC$. Dokažite da umnožak $|BF| \cdot |CG|$ ne ovisi o položaju točke $A$.