MathDB

Triangle

ABC

has

AB=21

AC=22

, and

BC=20

. Points

D

and

E

are located on

\overline{AB}

and

\overline{AC}

, respectively, such that

\overline{DE}

is parallel to

\overline{BC}

and contains the center of the inscribed circle of triangle

ABC

. Then

DE=m/n

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement