2002 AIME II Problem 14

The perimeter of triangle A P M is 152 , and angle P A M is a right angle. A circle of radius 19 with center O on \overline{A P} is drawn so that it is tangent to \overline{A M} and \overline{P M}. Given that O P=m / n, where m and n are relatively prime positive integers, find m+n.