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Same area and same perimeter => two equal sides

Source: Brazilian Math Olympiad, 2002

November 15, 2005
geometryperimetercyclic quadrilateralgeometry unsolved

Problem Statement

ABCDABCD is a cyclic quadrilateral and MM a point on the side CDCD such that ADMADM and ABCMABCM have the same area and the same perimeter. Show that two sides of ABCDABCD have the same length.
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