MathDB

The four points in S are collinear

Source: Baltic Way 2002

November 13, 2010

inequalitiesabsolute valuetriangle inequalitycombinatorics proposedcombinatorics

Problem Statement

A set

S

of four distinct points is given in the plane. It is known that for any point

X\in S

the remaining points can be denoted by

Y,Z

and

W

so that

|XY|=|XZ|+|XW|

Prove that all four points lie on a line.