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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

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Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

Circle Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The arrangement of the circles in the diagram is worthy of some discussion. How do we know the surrounding rectangle is a square and that the arrangement gives us the smallest square?