Marinada '22

[lang=hr] Dan je trapez $ABCD$ u kome je $AD \parallel BC$. Kružnica koja prolazi kroz vrhove $B,C$ siječe stranice $AB,CD$ u točkama $X,Y$ i dodiruje osnovicu $AD$ u $K$. Poznato je da je $\angle BKC = 50^{\circ}$ i $\angle ABK=\angle KDC$. Odredi $\angle XKY$. (rješenje zapišite u stupnjevima bez mjerne jedinice npr. "45") [/lang] [lang=en] In a trapezoid $ABCD$ we have $AD \parallel BC$. Denote the points at which the circle passing through points $B,C$ intersects sides $AB,CD$ as $X,Y$ and denote the point at which it touches base $AD$ as $K$. It is known that $\angle BKC = 50^{\circ}$ and $\angle ABK=\angle KDC$. Determine $\angle XKY$. (Write the solution in degrees but without measuring unit, e.g. "45".) [/lang]