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Area of AMNQ is maximal [ILL 1977]

Source:

January 11, 2011
geometrygeometry unsolved

Problem Statement

A square ABCDABCD is given. A line passing through AA intersects CDCD at QQ. Draw a line parallel to AQAQ that intersects the boundary of the square at points MM and NN such that the area of the quadrilateral AMNQAMNQ is maximal.
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