Evelyn C. The Seven Circles Theorem and other new theorems 1974

Textbook in PDF format

This collection of theorems in plane geometry, some of which we believe to be new, illustrates that there may still be plenty of interesting theorems awaiting discovery. We derived a lot of enjoyment from evolving them (or, as it transpired in some cases, rediscovering them) and it is our sincere hope that the reader may derive as much pleasure from reading about them.
Projective addition of vectors and the dual theory
Point-point vectors
Line-line vectors
Extensions of Pascal's and Brianchon's theorems
The heptagon theorem
The three-conics theorem
The double-contact theorem
The four-conics theorem
Inscribed octagons
Chains of circles
The seven circles theorem
A theorem about two parallel straight lines and six circles
A theorem about a triangle and six circles
The nine circles theorem