Question 15
A circular cone with vertex $C$ has point $A$ on the circumference of its base and point $B$ on the segment $AC$, as shown in the diagram below. The shortest possible rope is wrapped once around the cone such that it starts at point $A$ and ends at point $B$. Assume that the base diameter and the slant height of this cone are $6$ cm and $12$ cm, respectively. If $AB=3$ cm and $D$ is the point on the rope that is closest to $C$, what is the length, in cm, of $CD$?
