A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
A triangle PQR, right angled at P, slides on a horizontal floor
with Q and R in contact with perpendicular walls. What is the locus
You need to use the fact that if two circles touch then the line
joining their centres goes through the point at which they touch.
(Why is that?) Then join the centres of all the 'petals' to the
centre of the inner circle and draw the hexagon formed by joining
the centres of adjacent 'petals' as in the sketch. After that the
proof depends on finding similar triangles.