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Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Giant Holly Leaf

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

Two Shapes & Printer Ink

Stage: 4 Challenge Level: Challenge Level:1

two shapes plus a grid

Hint 1 - Does a grid help?

Hint 2 - Pick out parts from circles (arcs). Where is the centre for each of those circles?