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Points moving on two lines with constant speed, common point of circles

Source: Bundeswettbewerb Mathematik 2020, Round 2 - Problem 3

November 17, 2020
geometrygeometry proposedcircumcirclecyclic quadrilateralmoving points

Problem Statement

Two lines mm and nn intersect in a unique point PP. A point MM moves along mm with constant speed, while another point NN moves along nn with the same speed. They both pass through the point PP, but not at the same time.
Show that there is a fixed point Q≠PQ \ne P such that the points P,Q,MP,Q,M and NN lie on a common circle all the time.
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