Marinada '22

[lang=hr] Dan je raznostranični trokut $ABC$ s opisanom kružnicom $k$ i opsegom $240$. Točke $D,E$ su središta lukova $ABC$ i $ACB$ kružnice $k$. Tangenta u $A$ na kružnicu $k$ siječe polupravac $DE$ u $F$. Poznato je da polovište dužine $AF$ leži na $BC$. Odredi duljinu $BC$. [/lang] [lang=en] A scalene triangle $ABC$ with circumscribed circle $k$ and perimeter $240$ is given. The points $D,E$ are the centers of the arcs $ABC$ and $ACB$ of the circle $k$. The tangent at $A$ to the circle $k$ intersects the ray $DE$ at $F$. It is known that the midpoint of $AF$ lies on $BC$. Determine the length of $BC$. [/lang]