2007 AIME II Problem 15

Four circles \omega, \omega_{A}, \omega_{B}, and \omega_{C} with the same radius
are drawn in the interior of triangle A B C such that \omega_{A} is tangent to sides A B and A C, \omega_{B} to B C and B A, \omega_{C} to C A and C B, and \omega is externally tangent
to \omega_{A}, \omega_{B}, and \omega_{C}. If the sides of triangle A B C are 13,14 , and 15 , the
radius of \omega can be represented in the form \frac{m}{n}, where m and n are relatively prime positive integers.
Find m+n.