BD-BDMO 2015 Problem 6

Trapezoid $ABCD$ has sides $AB=92,BC=50,CD=19,AD=70$ $AB$ is parallel to $CD$ A circle with center $P$ on $AB$ is drawn tangent to $BC$ and $AD$ .Given that $AP=\dfrac mn$ (Where $m,n$ are relatively prime).What is $m+n$ ?