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intersecting rays, antiparallels, angle bisectors, find point

Source: Spanish Mathematical Olympiad 1985 P6

August 2, 2018
geometryangle bisector

Problem Statement

Let OXOX and OYOY be non-collinear rays. Through a point AA on OXOX, draw two lines r1r_1 and r2r_2 that are antiparallel with respect to ∠XOY\angle XOY. Let r1r_1 cut OYOY at MM and r2r_2 cut OYOY at NN. (Thus, ∠OAM=∠ONA\angle OAM = \angle ONA). The bisectors of ∠AMY \angle AMY and ∠ANY\angle ANY meet at PP. Determine the location of PP.
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