Question 177
Let $A$, $B$, $C$ and $D$ be four points lying on a circle in this order. Suppose there is a point $K$ on the segment $A B$ such that $B D$ bisects the segment $K C$ and $A C$ bisects the segment $K D$. Determine the smallest possible value that $\left|\frac{A B}{C D}\right|$ can take.