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2 lines as area bisectors given , segment bisector wanted, in a convex ABCD

Source: 2012 Dutch BxMO / EGMO TST p4

September 19, 2018
geometryareasequal segments

Problem Statement

Let ABCDABCD a convex quadrilateral (this means that all interior angles are smaller than 180o180^o), such that there exist a point MM on line segment ABAB and a point NN on line segment BCBC having the property that ANAN cuts the quadrilateral in two parts of equal area, and such that the same property holds for CMCM. Prove that MNMN cuts the diagonal BDBD in two segments of equal length.
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