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Find the locus

Source: 5-th Taiwanese Mathematical Olympiad 1996

January 12, 2007
geometryperpendicular bisectorangle bisectorgeometry unsolved

Problem Statement

Let be given points A,BA,B on a circle and let PP be a variable point on that circle. Let point MM be determined by PP as the point that is either on segment PAPA with AM=MP+PBAM=MP+PB or on segment PBPB with AP+MP=PBAP+MP=PB. Find the locus of points MM.
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