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if intersections of sidelines & diagonals pass through centroid => trapezoid

Source: 2009 Sharygin Geometry Olympiad Final Round problem 2 grade 10

July 26, 2018
geometrytrapezoid

Problem Statement

Given quadrilateral ABCDABCD. Its sidelinesAB AB and CDCD intersect in point KK. It's diagonals intersect in point LL. It is known that line KLKL pass through the centroid of ABCDABCD. Prove that ABCDABCD is trapezoid.
(F.Nilov)
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