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?

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.