Točka
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
je unutar kvadrata
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
. Označimo s
![A_1](/media/m/5/a/6/5a6ce1347567551c02239ff8d4ebee67.png)
,
![B_1](/media/m/5/d/9/5d9518a7c0ead344571aac61b51bb25c.png)
,
![C_1](/media/m/b/0/b/b0b10dc32c3e01824e0f0b6753ac2537.png)
,
![D_1](/media/m/f/e/6/fe67388584f844e56a8db45e4e8768ca.png)
druge točke presjeka pravaca
![AM](/media/m/9/2/1/921d54bb92ada2d2120b2591b722ea12.png)
,
![BM](/media/m/9/b/a/9ba306de3378f6c32d1ba470951ff4a4.png)
,
![CM](/media/m/f/f/2/ff25b5f32e58e1da5c58d0d512c4e808.png)
,
![DM](/media/m/b/2/8/b28f740f871a84995535c1b1d29b160e.png)
, tim redom, s kružnicom opisanom kvadratu
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
. Dokažite da je
%V0
Točka $M$ je unutar kvadrata $ABCD$. Označimo s $A_1$, $B_1$, $C_1$, $D_1$ druge točke presjeka pravaca $AM$, $BM$, $CM$, $DM$, tim redom, s kružnicom opisanom kvadratu $ABCD$. Dokažite da je
$$|A_1B_1||C_1D_1| = |A_1D_1||B_1C_1|\text{.}$$