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There are **7** NRICH Mathematical resources connected to **Arithmetic, geometric and harmonic means**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### Mean Geometrically

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Classical Means

Use the diagram to investigate the classical Pythagorean means.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### About Pythagorean Golden 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?

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Three Ways

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pythagorean Golden 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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Without Calculus

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.

Age 16 to 18

Challenge Level