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. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by
replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
A right-angled isosceles triangle whose two equal sides are 2
units in length is attached at its right-angled vertex to the
centre of a square of side 2 units and rotated about this centre
What can you say about the area of the part of the square
covered by the triangle as it rotates?
What happens to this area if the triangle is reduced in size so
that its two equal sides are $ \sqrt 2 $ units?