MathDB

The sum of lengths does not exceed the perimeter

Source: International Zhautykov Olympiad 2013 - D2 - P2

January 17, 2013

geometryhexagon

Problem Statement

Given convex hexagon

ABCDEF

with

AB \parallel DE

BC \parallel EF

, and

CD \parallel FA

. The distance between the lines

AB

and

DE

is equal to the distance between the lines

BC

and

EF

and to the distance between the lines

CD

and

FA

. Prove that the sum

AD+BE+CF

does not exceed the perimeter of hexagon

ABCDEF