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38th Austrian Mathematical Competition 2007

Source: 1st round

February 7, 2009
geometry unsolvedgeometry

Problem Statement

Let M M be the intersection of the diagonals of a convex quadrilateral ABCD ABCD. Determine all such quadrilaterals for which there exists a line g g that passes through M M and intersects the side AB AB in P P and the side CD CD in Q Q, such that the four triangles APM APM, BPM BPM, CQM CQM, DQM DQM are similar.
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