MathDB

2 XY <= AB+ A'B" , midpoints inequality by 3 pairs of parallel lines

Source: Flanders Math Olympiad 1987 p2

December 24, 2022

geometrygeometric inequality

Problem Statement

Two parallel lines

a

and

b

meet two other lines

c

and

d

. Let

A

and

A'

be the points of intersection of

a

with

c

and

d

, respectively. Let

B

and

B'

be the points of intersection of

b

with

c

and

d

, respectively. If

X

is the midpoint of the line segment

A A'

and

Y

is the midpoint of the segment

BB'

, prove that

|XY| \le \frac{|AB|+|A'B'|}{2}.