MathDB

AQ = BQ [intersections of lines through Q with cube surface]

Source: Austrian MO 2005 round 2

June 27, 2005

geometry3D geometrygeometric transformationreflectionPutnamgeometry solved

Problem Statement

Let

Q

be a point inside a cube. Prove that there are infinitely many lines

l

so that

AQ=BQ

where

A

and

B

are the two points of intersection of

l

and the surface of the cube.