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Let ABCDEF be a convex hexagon. Let A', B', C', D', E', F' be the centroids of triangles FAB, ABC, BCD, CDE, DEF, EFA, respectively.

(a) Show that every pair of opposite sides in hexagon A', B', C', D', E', F' are parallel and equal in length.

 

https://latex.artofproblemsolving.com/e/0/a/e0aa5e170c143140f45288af94c7c4e4dee30b6e.png

 Jan 31, 2021
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This is easy using coordinates.

 Feb 3, 2021

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