3

Part of 2002 Regional Competition For Advanced Students

Problems(1)

perimeter inequality in convex hegaxon , 1/2 \le s/(u+v) \le 1

Source: Austrian Regional Competition For Advanced Students 2002 p3

ABCDEF

(has all interior angles less than

180^o

) with the perimeter

s

ACE

BDF

have perimeters

u

v

respectively. a) Show the inequalities

\frac{1}{2} \le \frac{s}{u+v}\le 1

b) Check whether

1

is replaced by a smaller number or

1/2

by a larger number can the inequality remains valid for all convex hexagons.

geometryperimeterinequalitiesconvexhexagongeometric inequality