RU-ALLRUSSIAN 1975 Problem 5
Given a convex hexagon, take the midpoint of each of the six diagonals joining vertices which are separated by a single vertex (so if the vertices are in order A, B, C, D, E, F, then the diagonals are AC, BD, CE, DF, EA, FB). Show that the midpoints form a convex hexagon with a quarter the area of the original.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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