Marinada '24

[lang=hr] Dana je kružnica $\sigma$ radijusa $1$ sa središtem u $A$ te točka $B$ na kružnici. Neka je $C$ polovište dužine $\overline{AB}$ i neka okomica na $AB$ u $A$ siječe $\sigma$ u $D$ i $F.$ Dužina $\overline{CD}$ siječe kružnicu promjera $\overline{AB}$ u $E.$ Kružnica sa središtem u $D$ i polumjerom $\overline{DE}$ siječe $\sigma$ u $H$ i $G.$ Odredi kut $\angle HAG.$ Odgovor treba napisati u stupnjevima, i treba napisati samo broj (dakle ako je odgovor $123^\circ,$ treba upisati samo 123). [/lang] [lang=en] Given a circle $\sigma$ with a radius of $1$ centered at $A$ and a point $B$ on the circle. Let $C$ be the midpoint of the segment $\overline{AB}$, and let a perpendicular to $AB$ at $A$ intersect $\sigma$ at points $D$ and $F$. The segment $\overline{CD}$ intersects the circle with diameter $\overline{AB}$ at point $E$. The circle centered at $D$ with radius $\overline{DE}$ intersects $\sigma$ at points $H$ and $G$. Determine the angle $\angle HAG$. The answer should be written in degrees, and only the number should be provided (so if the answer is $123^\circ$, you should just write 123). [/lang]