MathDB
equal areas of triangles in ABCD leads to parallel lines

Source: 2013 Dutch BxMO / EGMO TST p1

September 19, 2018
geometryareasparallelequal area

Problem Statement

In quadrilateral ABCDABCD the sides ABAB and CDCD are parallel. Let MM be the midpoint of diagonal ACAC. Suppose that triangles ABMABM and ACDACD have equal area. Prove that DM//BCDM // BC.