Marinada '26

[lang=hr] Neka je $AF$ visina jednakokračnog šiljastokutnog trokuta $\triangle ABC$ s osnovicom $BC$, a točka $O$ središte njemu opisane kružnice. Ako je $D$ nožište okomice iz točke $A$ na pravac $BO$, a $M$ polovište stranice $\lvert AC\rvert$ te $\measuredangle BAC= 30^\circ$, odredi $\measuredangle DMC$. [/lang] [lang=en] Let $AF$ be the altitude of an isoceles acute triangle $\triangle ABC$ with base $BC$, and let $O$ be its circumcenter. Let $D$ be the foot of altitude from $A$ to the line $BO$. Let $M$ be the midpoint $\lvert AC\rvert$. Assume $\measuredangle BAC= 30^\circ$, find $\measuredangle DMC$. [/lang]