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Find range of the max/min of diagonals in ABCDEF

Source: Japanese MO Finals 1999

August 5, 2010
trigonometrygeometryrhombusgeometry proposed

Problem Statement

All sides of a convex hexagon ABCDEFABCDEF are 11. Let M,mM,m be the maximum and minimum possible values of three diagonals AD,BE,CFAD,BE,CF. Find the range of MM, mm.
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