MathDB

\triangle ABC

let

I

be the center of the inscribed circle, and let the bisector of

\angle ACB

intersect

AB

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 = \tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p + q

Problem Statement