Neka je točka
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
nožište visine iz vrha
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
šiljastokutnog trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
, točke
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
i
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
redom nožišta okomica iz točke
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
na stranice
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
i
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
, a točka
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
središte opisane kružnice danog trokuta. Ako vrijedi
![\left\vert AC \right\vert = 2\left\vert OP \right\vert](/media/m/c/8/b/c8b9dc92338b0f6639e0cec3c5b06b2c.png)
, dokaži da vrijedi
![\left\vert AB \right\vert = 2\left\vert OQ \right\vert](/media/m/3/2/d/32d419a2d7195891cfd7bdd67d189a54.png)
.
%V0
Neka je točka $N$ nožište visine iz vrha $A$ šiljastokutnog trokuta $ABC$, točke $P$ i $Q$ redom nožišta okomica iz točke $N$ na stranice $\overline{AB}$ i $\overline{AC}$, a točka $O$ središte opisane kružnice danog trokuta. Ako vrijedi $\left\vert AC \right\vert = 2\left\vert OP \right\vert$, dokaži da vrijedi $\left\vert AB \right\vert = 2\left\vert OQ \right\vert$.