1992 AIME Problem 9

Trapezoid A B C D has sides A B=92, B C=50, C D=19, and A D=70, with \overline{A B} parallel to \overline{C D}. A circle with center P on \overline{A B} is drawn tangent to \overline{B C} and \overline{A D}. Given that A P=m / n, where m and n are relatively prime positive integers, find m+n.