Na gornjem dijelu kružnice sa središtem
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
nalaze se točke
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
,
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
,
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
,
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
, tako da je
![\angle AOB=60^\circ](/media/m/9/2/8/9281aa706d158dcb6a765977bf4fe2a1.png)
,
![\angle AOC=90^\circ](/media/m/7/3/6/736e16ab6f58615d8620c731bf51cdf0.png)
,
![\angle AOD=120^\circ](/media/m/3/a/7/3a7a8498f26905a0d4ca61c608a206df.png)
,
![\angle AOE=180^\circ](/media/m/8/1/e/81eea4a7f292e9d01373ea72fc62db01.png)
. Ako je
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
točka koja dijeli polumjer
![\overline{OA}](/media/m/1/0/4/104359455117bb4ea7ab044d1f42a4ad.png)
u omjeru zlatnog reza, tj.
![|OP|:|PA|=|PA|:|OA|](/media/m/f/4/0/f40b2f0ef0e70f9ff9bfb7ded58b4649.png)
, odredite međusobne omjere kvadrata udaljenosti
![|PA|^2](/media/m/2/8/a/28a4172e82266dfae64cad884b5d6c67.png)
,
![|PB|^2](/media/m/b/a/4/ba476646ba322fc4d1ebdd27152f6949.png)
,
![|PC|^2](/media/m/c/d/b/cdba26d1d2b58f2faf3789778b2e4538.png)
,
![|PD|^2](/media/m/6/a/9/6a9f67643ac3981e130e99f8bb7ae9eb.png)
,
![|PE|^2](/media/m/5/4/6/5467f76e22de6448c1f8540bca6d867c.png)
.
%V0
Na gornjem dijelu kružnice sa središtem $O$ nalaze se točke $A$, $B$, $C$, $D$, $E$, tako da je $\angle AOB=60^\circ $, $\angle AOC=90^\circ $, $\angle AOD=120^\circ $, $\angle AOE=180^\circ $. Ako je $P$ točka koja dijeli polumjer $\overline{OA}$ u omjeru zlatnog reza, tj. $|OP|:|PA|=|PA|:|OA|$, odredite međusobne omjere kvadrata udaljenosti $|PA|^2$, $|PB|^2$, $|PC|^2$, $|PD|^2$, $|PE|^2$.