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center of gravity of quad coincide

Source: Polish MO Finals 1958 p2

August 29, 2024
geometryCentroidcenter of gravity

Problem Statement

Each side of a convex quadrilateral ABCD ABCD is divided into three equal parts; a straight line is drawn through the dividing points of sides AB AB and AD AD that lie closer to vertex A A , and similarly for vertices B B , C C , D D . Prove that the center of gravity of the quadrilateral formed by the drawn lines coincides with the center of gravity of quadrilateral ABCD ABCD .
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