Dan je trokut
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
takav da je
![|AC| \neq |BC|](/media/m/5/d/0/5d063e279b5bec6873b097909529ae86.png)
. Neka je
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
polovište stranice
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
,
![\alpha = \angle BAC, \beta = \angle ABC, \varphi = \angle ACM, \psi = \angle BCM](/media/m/6/5/9/659c39ed6788d62d129a7f80f6c11bcb.png)
. Dokažite da je
%V0
Dan je trokut $ABC$ takav da je $|AC| \neq |BC|$. Neka je $M$ polovište stranice $\overline{AB}$, $\alpha = \angle BAC, \beta = \angle ABC, \varphi = \angle ACM, \psi = \angle BCM$. Dokažite da je
$$\frac{\sin \alpha \sin \beta}{\sin(\alpha - \beta)} = \frac{\sin \varphi \sin \psi}{\sin (\varphi - \psi)}.$$