Lozanovski S. A Beautiful Journey Through Olympiad Geometry

Ver. 1.3 - olympiadgeometry.com, 2018. - 195 p.This book is aimed at anyone who wishes to prepare for the geometry part of the mathematics competitions and Olympiads around the world. No previous knowledge of geometry is needed. Even though I am a fan of non-linear storytelling, this book progresses in a linear way, so everything that you need to know at a certain point will have been already visited before. We will start our journey with the most basic topics and gradually progress towards the more advanced ones. The level ranges from junior competitions in your local area, through senior national Olympiads around the world, to the most prestigious International Mathematical Olympiad. The word ”Beautiful” in the book’s title means that we will explore only synthetic approaches and proofs, which I find elegant and beautiful. We will not see any analytic approaches, such as Cartesian or barycentric coordinates, nor we will do complex number or trigonometry bashing.
This book is structured in two parts. The first one provides an introduction to concepts and theorems. For the purpose of applying these concepts and theorems to geometry problems, a number of useful properties and examples with solutions are offered. At the end of each chapter, a selection of unsolved problems is provided as an exercise and a challenge for the reader to test their skills in relation to the chapter topics. This part can be roughly divided in two portions: Junior (the first 10 chapters) and Senior (the other 14 chapters). The second part of this book contains mixed problems, mostly from competitions and Olympiads from all around the world.Congruence of Triangles.
Angles of a Transversal.
Area of Plane Figures.
Similarity of Triangles.
Circles.
A Few Important Centers in a Triangle.
Excircles.
Collinearity.
Concurrence.
A Few Useful Lemmas.
Basic Trigonometry.
Power of a Point.
Collinearity II.
Concurrence II.
Symmedian.
Homothety.
Mixtilinear Incircles.
Inversion.
Pole & Polar.
Complete quadrilateral.
Spiral Similarity.
Harmonic Ratio.
Feuerbach’s Theorem.
Apollonius’ Problem.
Mixed Problems.
A Contests Abbreviations.True PDF