MathDB

12

Part of 2002 Baltic Way

Problems(1)

The four points in S are collinear

Source: Baltic Way 2002

11/13/2010
A set SS of four distinct points is given in the plane. It is known that for any point X∈SX\in S the remaining points can be denoted by Y,ZY,Z and WW so that ∣XY∣=∣XZ∣+∣XW∣|XY|=|XZ|+|XW| Prove that all four points lie on a line.
inequalitiesabsolute valuetriangle inequalitycombinatorics proposedcombinatorics