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
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
This is another tough nut and perhaps the diagram of the 50p
piece will help.