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PAMO 2016 Q5

Source: PAMO 2016

April 29, 2016
geometrymidpointtrapezoid

Problem Statement

Let ABCDABCD be a trapezium such that the sides ABAB and CDCD are parallel and the side ABAB is longer than the side CDCD. Let MM and NN be on the segments ABAB and BCBC respectively, such that each of the segments CMCM and ANAN divides the trapezium in two parts of equal area. Prove that the segment MNMN intersects the segment BDBD at its midpoint.
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