Take any four points A, B, C, D in the plane, no three of which are collinear.
They describe a unique quadrilateral, if we take the points as being its vertices.
But they also describe a square, if we require only that the points lie on its sides.
Using a compass and straightedge, construct a square such that the four points lie, one each, on its sides
Edit: or the extensions of its sides.
Hint: The points are not special.
Draw four similar points and do the construction on a sheet of paper if that helps.
The answer would then be to describe the process.
Edited by bonanova, 07 June 2014 - 12:25 AM.
Relax the constraints