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Why do this
problem?

Doing this problem you need to visualise the relationship between the formulae for the arithmetic, geometric and harmonic means in terms of the radius of a circle and the geometry of similar triangles and Pythagoras Theorem. This process involves a beautiful blend of algebra and geometry. It provides a good exercise for learners in mathematical reasoning and proof. The mathematical concepts are simple and the interplay of ideas to give the necessary proofs is good experience for learners. 