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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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Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

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Find the vertices of a pentagon given the midpoints of its sides.

Tracking Points

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
By viewing the 3-D coordinates as if you could not see the third dimension you can extend what is happening in the 2D case and this is explored in the problem Coordinate Patterns first published in September 2004.