If three identical circles pass
through a common point, P, then their other three intersections lie on another
circle, of the same size. Can you prove it?
This is known as Johnson's theorem, first published in 1916.
This diagram illustrates the proof. Can you see it?
If three identical circles pass
through a common point, P, then their other three intersections lie on another
circle, of the same size. Can you prove it?