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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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The Rescaled Map

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

Conical Bottle

Stage: 4 Challenge Level: Challenge Level:1

A right circular cone is filled with liquid to a depth of half its vertical height.

The cone is inverted. How high up the vertical height of the cone will the liquid rise?