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Thejas, (1) Draw an accurate sketch, including the circle, the hexagon, and the long diagonals of the hexagon, and you should be able to guess how the radius of the circle relates to the perimeter of the hexagon. To prove this, use symmetry and the fact that a regular hexagon has angles of 120 degrees and a regular (equilateral) triangle has angles of 60 degrees. (2) Now use the usual formula C = 2 π r for the circumference. Good Hunting!
 


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