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Cut Cube

Find the shape and symmetries of the two pieces of this cut cube.

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Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

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Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Logosquares

Stage: 5 Challenge Level: Challenge Level:1

Why do this problem?
A simple trig. calculation involving cot and tan.

Key question
How many squares in each ring? So what are the angles?

Can you find any right angled triangles?