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?
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?