MathDB

Let A

BC

be a triangle with

AB = 5, AC = 4, BC = 6

. The internal angle bisector of

C

intersects the side

AB

D

. Points

M

and

N

are taken on sides

BC

and

AC

, respectively, such that

DM\parallel AC

and

DN \parallel BC

. If

(MN)^2 =\frac{p}{q}

where

p

and

q

are relatively prime positive integers then what is the sum of the digits of

|p - q|

9