Question 6
In $\triangle ABC$ let $I$ be the center of the inscribed circle, and let the bisector of $\angle ACB$ intersect $\overline{AB}$ at $L.$ The line through $C$ and $L$ intersects the circumscribed circle of $\triangle ABC$ at the two points $C$ and $D.$ If $LI = 2$ and $LD = 3,$ then $IC = \frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$