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Find a point M such that the triangles are congruent

Source: IMO LongList 1970 - P46

May 22, 2011
geometry proposedgeometry

Problem Statement

Given a triangle ABCABC and a plane π\pi having no common points with the triangle, find a point MM such that the triangle determined by the points of intersection of the lines MA,MB,MCMA,MB,MC with π\pi is congruent to the triangle ABCABC.
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