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Matter of Scale

Prove Pythagoras' Theorem using enlargements and scale factors.

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Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

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Flower Show

Weekly Problem 7 - 2006
It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?

Conical Bottle

Stage: 4 Challenge Level: Challenge Level:1
What fraction of liquid is present compared to a completely full cone?