Question 43
Let $k$ be a circle with centre $M$ and let $A B$ be a diameter of $k$. Furthermore, let $C$ be a point on $k$ such that $A C = A M$. Let $D$ be the point on the line $A C$ such that $C D = A B$ and $C$ lies between $A$ and $D$. Let $E$ be the second intersection of the circumcircle of $B C D$ with line $A B$ and $F$ be the intersection of the lines $E D$ and $B C$. The line $A F$ cuts the segment $B D$ in $X$. Determine the ratio $B X / X D$.