Na hipotenuzi
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
pravokutnog trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
izabrana je točka
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
tako da je
![|PA|=m](/media/m/6/b/6/6b6937a4313c99bb9ed6144f315e43ff.png)
,
![|PB|=n](/media/m/2/2/b/22bb75071e149153280e7d27a3629383.png)
,
![|PC|=d](/media/m/5/b/5/5b583909bef611c8684eada2bf951d85.png)
. Pokažite da je
![a^2m^2 + b^2n^2 = c^2d^2\text{,}](/media/m/4/6/f/46f19f37390c2d23b379ba86712f5305.png)
gdje je
![|BC|=a](/media/m/9/3/7/9373ed7cff2c7459a7da8228308660a5.png)
,
![|CA|=b](/media/m/a/9/5/a95918bb12f2e8be1424f9a4313ecc11.png)
,
![|AB|=c](/media/m/d/7/b/d7b5ae961be7252a962f273185136ea9.png)
.
%V0
Na hipotenuzi $\overline{AB}$ pravokutnog trokuta $ABC$ izabrana je točka $P$ tako da je $|PA|=m$, $|PB|=n$, $|PC|=d$. Pokažite da je
$$a^2m^2 + b^2n^2 = c^2d^2\text{,}$$
gdje je $|BC|=a$, $|CA|=b$, $|AB|=c$.