2001 AIME I Problem 7

Triange A B C has A B=21, A C=22, and B C=20. Points D and E are located on \overline{A B} and \overline{A C}, respectively, such that \overline{D E} is parallel to \overline{B C} and contains the center of the inscribed circle of triangle A B C. Then D E=m / n, where m and n are relatively prime positive integers. Find m+n.