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Determine the set of all acceptable points

Source: Austrian Mathematical Olympiad 2008 Problem 6

February 6, 2009
geometrycircumcirclegeometric transformationreflectiongeometry unsolved

Problem Statement

We are given a square ABCD ABCD. Let P P be a point not equal to a corner of the square or to its center M M. For any such P P, we let E E denote the common point of the lines PD PD and AC AC, if such a point exists. Furthermore, we let F F denote the common point of the lines PC PC and BD BD, if such a point exists. All such points P P, for which E E and F F exist are called acceptable points. Determine the set of all acceptable points, for which the line EF EF is parallel to AD AD.
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