MathDB

No line intersects four lines in a cube ABCDA'B'C'D'

Source: Vietnam MO 1982 P6

March 17, 2011

geometry3D geometrygeometry unsolved

Problem Statement

Let

ABCDA'B'C'D'

be a cube (where

ABCD

and

A'B'C'D'

are faces and

AA',BB',CC',DD'

are edges). Consider the four lines

AA', BC, D'C'

and the line joining the midpoints of

BB'

and

DD'

. Show that there is no line which cuts all the four lines.