Two given line segments have the lengths a and b.
Using only a compass and an unmarked straightedge construct a line segment whose length is equal to the harmonic mean of a and b.

Construct a trapezoid whose parallel sides have 
lengths a and b. Construct a line through the 
intersection of the diagonals and parallel to 
the parallel sides.

The line segment determined by the intersections
of this line and the other two sides of the trapezoid 
is the line segment desired.

Posted by Bractals on 2014-06-17 13:40:15