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
Four rods of equal length are hinged at their endpoints to form a
rhombus. The diagonals meet at X. One edge is fixed, the opposite
edge is allowed to move in the plane. Describe the locus of the
point X and prove your assertion.
A blue coin rolls round two yellow coins which touch. The coins are
the same size. How many revolutions does the blue coin make when it
rolls all the way round the yellow coins? Investigate for a line of
Well done Luke and Daniel from year 9 together
with Nicholas and Luke from year 7 of Clevedon Community School who
sent in the following solution.
The locus of corner D will be a circle with a radius equal to
AD, whose centre is A. The locus of the point Y will be a circle
with a radius equal to AD, and a centre on AB one third of the way
along from A to B.
Can you see the reason for this? The locus of
Y is a circle. If you imagine a line joining Y to the centre Z of
this circle then DYZA is a parallelogram so ZY = AD and AZ=DY.