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MathNet 2013 Question 47

Math Olympiad Vault · MathNet 2013

Question 47

A regular hexagonal prism $ABCDEF A'B'C'D'E'F'$ has the edge $AB = 12$ and the height $AA' = 12\sqrt{3}$. Let $N$ be the midpoint of the edge $CC'$.

a.
Prove that the lines $BF'$ and $ND$ are perpendicular.

b.
Find the distance between the lines $BF'$ and $ND$.

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