construct any old trapezium (trapezoid in the US) and draw the two diagonals
at the point where the diagonals meet, construct a line parallel to the two parallel sides of the trapezium
what do you notice?
can you prove it?
this is an old problem, utilised in Michael de Villiers' excellent work on proof and geometry
use similar triangles to show that the length is the harmonic mean of 'a' and 'b'