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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.

Golden Triangle

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

Golden Powers

You add 1 to the golden ratio to get its square. How do you find higher powers?

Gold Again

Age 16 to 18
Challenge Level
Find all the angles and lengths in the diagram. Use the cosine rule.