# Harmonic Mean In an Isosceles Trapezoid

The harmonic mean of 2 numbers a and b is defined to be the reciprocal of the average (arithmetic mean) of these numbers' reciprocals. In essence, the harmonic mean of a and b = = . Prove that the segment drawn through the point of intersection of both diagonals of an isosceles trapezoid that is parallel to both bases is equal to the harmonic mean of the bases of this isosceles trapezoid. Can you prove this is true for ANY TRAPEZOID (and not just an isosceles trapezoid?)