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The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

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Another Triangle in a Triangle

Can you work out the fraction of the original triangle that is covered by the green triangle?

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Tuning and Ratio

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

Reductant Ratios

Age 16 to 18 Challenge Level:
The relative atomic masses of iron and oxygen are $56$ and $16$ respectively