Problem P4.2.3 replacement: a problem about harmonic sets.

There are several definitions of when four points, all lying on one line, 
form a harmonic set.  One definition given on page 60, in terms of 
Figure 4.7, though we did not stop to discuss that in class.  
However, another definition is given in Exercise 27, which we did discuss.

   If a rectangular towel is placed on the ground and you view it through
   a vertical picture plane, then the vanishing point of the long sides, 
   the vanishing point of the short sides, the vanishing point of one diagonal
   and the vanishing point of the other diagonal form a harmonic set of
   points on the horizon.  [In Figure 4.7, the perspective drawing of the
   towel is the quadrilateral CEXD and the horizon is the line AFBJ.]

On page 134, a set of points A, B, C, D is claimed to be harmonic.  Your job 
is to construct a quadrangle that demonstrates this is indeed a harmonic set.
That is, you need to find a quadrilateral with a pair of opposite sides
meeting at A, the other pair of opposite sides meeting at C, one diagonal
passing through B and one diagonal passing through D.  

You can do this by placing arbitrary lines and points, and by 
constructing lines through given pairs of points, and by labeling 
new points that arise as intersections of these.  In your figure,
you should be clear whether each new line or point is chosen arbitrarily
or is defined in terms of previously drawn lines and points.

In the end, you should arrive at what looks like the quadrangle you want,
but which only works if three points that look collinear do in fact lie
on a line.  YOU DON'T HAVE TO PROVE THAT THESE POINTS LIE ON A LINE, but
you do need to point out which three points must lie on a line in order
for your construction to be correct.