The figure above shows a semicircle with diameter AB
and center O. C is a point on AB, CE and OD are
perpendicular to AB, and CF is perpendicular
to OE. If AC = a and CB = b, prove that:

OD is the arithmetic mean of
a and b; AM(a,b).

CE is the geometric mean of
a and b; GM(a,b).

EF is the harmonic mean of a
and b; HM(a,b).

CD is the root mean square
of a and b; RMS(a,b)

Inequality: RMS (a,b) > AM (a,b) > GM (a,b)
> HM (a,b)

.
