Question 179
Let $A$ be a point and let $k$ be a circle through $A$. Let $B$ and $C$ be two further points on $k$. Furthermore, let $X$ be the intersection point of the bisector of $\angle A B C$ with $k$, and let $Y$ be the reflection of $A$ in the point $X$. Let $D$ be the intersection point of the line $Y C$ with $k$. Show that the point $D$ does not depend on the choice of $B$ and $C$ on the circle $k$.