MathDB

Romania District MO 2022 Grade 9 P4

Source: Romania District MO 2022 Grade 9

March 28, 2022

romaniageometryvector

Problem Statement

We call a set of

6

points in the plane splittable if we if can denote its elements by

A,B,C,D,E

and

F

in such a way that

\triangle ABC

and

\triangle DEF

have the same centroid.
[*]Construct a splittable set. [*]Show that any set of

7

points has a subset of

6

points which is not splittable.