Županijsko natjecanje 1997 SŠ3 3
Dodao/la:
arhiva1. travnja 2012. Ravnina siječe bočne bridove
![\overline{SA}](/media/m/5/0/c/50c5215cfb62a6425143e91081a3b26b.png)
,
![\overline{SB}](/media/m/1/f/0/1f0e7cde588fdb09aeb24fa9f31a3103.png)
,
![\overline{SC}](/media/m/3/6/0/360de3ab6a014c09c1f2fe5153210731.png)
i
![\overline{SD}](/media/m/2/2/6/22644aeda46f3d9f25bcc2126840d8f2.png)
pravilne četverostrane piramide u točkama
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
,
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
,
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
, tim redom. Dokažite da je
%V0
Ravnina siječe bočne bridove $\overline{SA}$, $\overline{SB}$, $\overline{SC}$ i $\overline{SD}$ pravilne četverostrane piramide u točkama $M$, $N$, $P$ i $Q$, tim redom. Dokažite da je $$
\frac{1}{|\overrightarrow {SM}|} + \frac{1}{|\overrightarrow {SP}|} =
\frac{1}{|\overrightarrow {SN}|} + \frac{1}{|\overrightarrow {SQ}|}.
$$
Izvor: Županijsko natjecanje iz matematike 1997