Question 29
Points $A$, $B$ and $C$ lie on a line in this order. For every circle $k$ passing through $B$ and $C$, let $D$ be one of the common points of $k$ and the bisector of $BC$. Furthermore, let $E$ be the second common point of the line $AD$ and $k$.
*Prove that the ratio $BE : CE$ is constant for all circles $k$.*
G. Baron, Vienna
*Prove that the ratio $BE : CE$ is constant for all circles $k$.*
G. Baron, Vienna