2002 AIME II Problem 14

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

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.