Duljine dviju stranica trokuta su
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
i
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
, njima nasuprotni kutovi su
![\alpha](/media/m/f/c/3/fc35d340e96ae7906bf381cae06e4d59.png)
i
![\beta](/media/m/c/e/f/cef1e3bcf491ef3475085d09fd7d291e.png)
, a visina na treću stranicu ima duljinu
![v](/media/m/3/d/c/3dc3003f5c10543e81344921fc032374.png)
.
![a)](/media/m/f/0/8/f0844437a160b45486aedcc02b92949d.png)
Ako za kutove vrijedi
![\alpha + \beta = \dfrac \pi 2](/media/m/5/b/b/5bbbcb05e8b2df22411e2af6a1985cd0.png)
ili
![|\alpha - \beta| = \dfrac \pi 2](/media/m/c/3/0/c3083d89082a1f73d0560ae5e89ccb72.png)
, dokaži da je
![\frac1{a^2}+\frac1{b^2}=\frac1{v^2}.](/media/m/1/4/c/14c211a7b4b733a839f1f4b86a73ca52.png)
![b)](/media/m/d/2/f/d2f292cd6a69e9158afe71ba9d830da4.png)
Ako ova jednakost vrijedi za neki trokut, dokaži da za njegove kutove vrijedi
![\alpha + \beta = \dfrac \pi 2](/media/m/5/b/b/5bbbcb05e8b2df22411e2af6a1985cd0.png)
ili
![|\alpha - \beta| = \dfrac \pi 2](/media/m/c/3/0/c3083d89082a1f73d0560ae5e89ccb72.png)
.
%V0
Duljine dviju stranica trokuta su $a$ i $b$, njima nasuprotni kutovi su $\alpha$ i $\beta$, a visina na treću stranicu ima duljinu $v$.
$a)$ Ako za kutove vrijedi $\alpha + \beta = \dfrac \pi 2$ ili $|\alpha - \beta| = \dfrac \pi 2$, dokaži da je $$
\frac1{a^2}+\frac1{b^2}=\frac1{v^2}.
$$
$b)$ Ako ova jednakost vrijedi za neki trokut, dokaži da za njegove kutove vrijedi $\alpha + \beta = \dfrac \pi 2$ ili $|\alpha - \beta| = \dfrac \pi 2$.