1992 AIME Problem 9

Trapezoid ABCD^{}_{} has sides AB=92^{}_{}, BC=50^{}_{}, CD=19^{}_{}, and AD=70^{}_{}, with AB^{}_{} parallel to CD^{}_{}. A circle with center P^{}_{} on AB^{}_{} is drawn tangent to BC^{}_{} and AD^{}_{}. Given that AP^{}_{}=\frac mn, 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.