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Weird Trapezium problem

Source: Bangladesh National Mathematical Olympiad 2015

February 25, 2019
geometrycontestsBdmotrapeziumangles

Problem Statement

Trapezoid ABCDABCD has sides AB=92,BC=50,CD=19,AD=70AB=92,BC=50,CD=19,AD=70 ABAB is parallel to CDCD A circle with center PP on ABAB is drawn tangent to BCBC and ADAD.Given that AP=mnAP=\dfrac mn (Where m,nm,n are relatively prime).What is m+nm+n?
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