Lozanovski S. A Beautiful Journey Through Olympiad Geometry

Olympiadgeometry.com: 2016. — 145 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.Congruence of Triangles.
Angles of a Transversal.
Area of Plane Figures.
Similarity of Triangles.
Circles.
Few Important Centers in a Triangle.
Exercises.
A Few Useful Lemmas.
Basic Trigonometry.
Power of a Point.
Collinearity.
Concurrence.
Symmedian.
Homothety.
Inversion.
Pole & Polar.
Complete quadrilateral.
Harmonic Ratio.
Feuerbach’s Theorem.
Apollonius’ Problem.
Mixed Problems.