Mock AIME 1 2006-2007 Problems/Problem 1

1. $\triangle ABC$ has positive integer side lengths of $x$ , $y$ , and $17$ . The angle bisector of $\angle BAC$ hits $BC$ at $D$ . If $\angle C=90^\circ$ , and the maximum value of $\frac{[ABD]}{[ACD]}=\frac{m}{n}$ where $m$ and $n$ are relatively prime positive intgers, find $m+n$ . (Note $[ABC]$ denotes the area of $\triangle ABC$ ).