MathDB

Let

E

be a finite set of points in space such that

E

is not contained in a plane and no three points of

E

are collinear. Show that

E

contains the vertices of a tetrahedron

T = ABCD

such that

T \cap E = \{A,B,C,D\}

(including interior points of

T

) and such that the projection of

A

onto the plane

BCD

is inside a triangle that is similar to the triangle

BCD

and whose sides have midpoints

B,C,D.

Problem Statement