5

Part of 1999 Japan MO Finals

Problems(1)

Find range of the max/min of diagonals in ABCDEF

Source: Japanese MO Finals 1999

All sides of a convex hexagon

ABCDEF

1

M,m

be the maximum and minimum possible values of three diagonals

AD,BE,CF

. Find the range of

M

m

trigonometrygeometryrhombusgeometry proposed