MathDB
Right Triangle and Circle

Source:

December 28, 2006
geometryperimetergeometric transformationdilationtrigonometrynumber theoryrelatively prime

Problem Statement

The perimeter of triangle APMAPM is 152,152, and the angle PAMPAM is a right angle. A circle of radius 1919 with center OO on AP‾\overline{AP} is drawn so that it is tangent to AM‾\overline{AM} and PM‾.\overline{PM}. Given that OP=m/n,OP=m/n, where mm and nn are relatively prime positive integers, find m+n.m+n.
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