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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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Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
Would it help to make a model?
What happens to the string when part of it is stopped by the shed?