There are **7** NRICH Mathematical resources connected to **Arithmetic, Geometric and Harmonic Means**, you may find related items under Algebraic expressions, equations and formulae.

Challenge Level

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?

Challenge Level

Use the diagram to investigate the classical Pythagorean means.

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?

Challenge Level

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

Challenge Level

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.

Challenge Level

Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.