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
The proof depends on identifying two sets of similar triangles
and spotting that they are arranged around the centre of the inner
circle in such a way that they can be used to show that they fit
together exactly as the angles add up to 360 degrees. The method is
elementary but calls for a systematic approach.