The fact that the envelope of the lines, dividing in two equal parts the quadrangle, is a hyperbola, is due to the fact that asymptotic triangles of a hyperbola have a constant area. Look at the file AsymptoticTriangle.html for a picture.

Look at the file ParaDivision.html for the solution of the special problem of a four-division of a parallelogram. In that case point F is always the center of the parallelogram. Which is the locus of F in the general case?

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