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O is centroid iff ABCD # - 1993 Cono Sur Shortlist G7

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October 24, 2021
geometryCentroidparallelogram

Problem Statement

Let ABCDABCD be a convex quadrilateral, where MM is the midpoint of DCDC, NN is the midpoint of BCBC, and OO is the intersection of diagonals ACAC and BDBD. Prove that OO is the centroid of the triangle AMNAMN if and only if ABCDABCD is a parallelogram.
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