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
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
As the triangle rotates compare what part of the square is not
covered by it anymore and what part of the square is newly
Does the triangle continue to cover the whole of the portion of
the square it moves over as its size reduces. What is special when
the triangles side is of length $ \sqrt 2 $ units?