Marinada '25

[lang=hr] Kružnica $k$ dodiruje kružnicu $l$ iznutra u točki $A$. Tetiva $\overline{BC}$ kružnice $l$ dodiruje kružnicu $k$ u točki $D$. Pravac $AD$ ponovno siječe kružnicu $l$ u točki $E$. Tangente iz točke $E$ na kružnicu $k$ sijeku kružnicu $l$ u točkama $F$ i $G$. Neka su $P$, $R$ i $S$ redom središta upisanih kružnica trokuta $BAC$, $BFC$ i $BGC$.Odredi $\angle ARP + \angle PSA$. (U stupnjevima) [/lang] [lang=en] Circle $k$ touches circle $l$ internally at point $A$. Chord $\overline{BC}$ of circle $l$ touches circle $k$ at point $D$. Line $AD$ meets circle $l$ again at point $E$. Tangents from $E$ to circle $k$ intersect circle $l$ at points $F$ and $G$. Let $P$, $R$, and $S$ be the incenters of triangles $BAC$, $BFC$, and $BGC$, respectively. Find $\angle ARP + \angle PSA$ (in degrees). [/lang]