Structure
Part I
  • theory explained (with proofs)
  • properties presented (with proofs)
  • solved examples to see the above "in action"
  • related problems for further practice
Part II
  • collection of olympiad problems
.Content
The lectures start from the very basics and progress step by step towards the advanced topics. Topics include:
  • Congruence, Similarity & Angles in Circles
  • Triangle Centers and their properties
  • Power of a Point & Radical Axis
  • Collinearity & Concurrence
  • Lemmas (Euler Line, 8-point circle, 9-point circle, ...)
  • Theorems (Ceva, Menelaus, Pascal, Desargues, Pappus)
  • Homothety & Spiral Similarity
  • Inversion, Pole & Polar, Duality
  • Mixtilinear & Curvilinear Incircles
  • Harmonic Ratio, Pencil & Quadrilateral
  • Isogonal Conjugates and related lemmas
  • Apollonian Circles
View the full Table of Contents in the Preview below.
Goal
  • Raise the Geometry knowledge of the students around the world, regardless of their financial background.
Price
Pay what you want!
By donating, you support me and this project; I would have the freedom to focus and spend more time sharing my olympiad knowledge and experience by improving this book (adding more examples, covering other topics of interest to you, maybe even writing a book on another olympiad topic) without being restricted by a 'standard' day job.
  • Don't donate if you are financially struggling and can't afford to or if you are not satisfied with the book contents.
  • Otherwise, your donations are welcome; Donate as much as the knowledge that you gained from this Journey is worth to you, of course, in your affordable range.
Feedback
Tell me what you think about the book and help me make this Journey even more beautiful. Write a general comment about the book, suggest a topic you'd like to see covered in a future version or report a mistake. Any feedback is welcome :)
© Stefan Lozanovski, 2016-2020