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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 $A'B'C'D'E'F'$ (namely $\overline{A'B'}$ and $\overline{D'E'},$ $\overline{B'C'}$ and $\overline{E'F'},$ and $\overline{C'D'}$ and $\overline{F'A'}$) are parallel and equal in length. (b) Show that triangles $A'C'E'$ and $B'D'F'$ have equal areas. Any help is appreciated !! Thanks in advance , I only want help in part A , not b , thanks

 Feb 1, 2021
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This is easy.  I solved it using coordinates.

 Feb 3, 2021

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