Dan je trokut ABCABCABC takav da je ∣AC∣≠∣BC∣|AC| \neq |BC|∣AC∣=∣BC∣. Neka je MMM polovište stranice AB‾\overline{AB}AB, α=∡BAC\alpha = \measuredangle BACα=∡BAC, β=∡ABC\beta = \measuredangle ABCβ=∡ABC, φ=∡ACM\varphi = \measuredangle ACMφ=∡ACM, ψ=∡BCM\psi = \measuredangle BCMψ=∡BCM. Dokažite da je sinαsinβsin(α−β)=sinφsinψsin(φ−ψ).\frac{\sin \alpha \sin \beta}{\sin(\alpha - \beta)} = \frac{\sin \varphi \sin \psi}{\sin(\varphi - \psi)}.sin(α−β)sinαsinβ=sin(φ−ψ)sinφsinψ.