A and B are two points on a circle centre O. Tangents at A and B
cut at C. CO cuts the circle at D. What is the relationship between
areas of ADBO, ABO and ACBO?
Use the diagram to investigate the classical Pythagorean means.
Show that the arithmetic mean, geometric mean and harmonic mean of
a and b can be the lengths of the sides of a right-angles triangle
if and only if a = bx^3, where x is the Golden Ratio.
What is the relationship between the arithmetic, geometric and
harmonic means of two numbers, the sides of a right angled triangle
and the Golden Ratio?