000RM.dvi

4.2 Harmonic mean 125

4.2 Harmonic mean ..................

LetABCDbe a trapezoid withAB//CD. If the diagonalsACandBD
intersect atK, and the line throughKparallel toABintersectADand
BCatPandQrespectively, thenPQis the harmonic mean ofABand
CD:
2
PQ

=

1

AB

+

1

CD

.

a

b

harmonic mean

P K Q

D C

A B

Another construction

a

b

harmonic mean