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 $$m+n$$.

(第二十届AIME2 2002 第14题)