2016 AIME I Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.