Question 199
Let $X Y Z$ be a triangle with $\angle X = 60^{\circ}$ and $\angle Y = 45^{\circ}$. A circle with center $P$ passes through points $A$ and $B$ on side $X Y$, $C$ and $D$ on side $Y Z$, and $E$ and $F$ on side $Z X$. Suppose $A B = C D = E F$. Find $\angle X P Y$ in degrees.