Imo Problems, Theorems, And Methods: Geometry (Mathematical Olympiad Series)

The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics. In the geometry volume, the IMO geometry problems are organized into seven chapters: "Similarity and Congruence," "Basic Properties of Circles and Four Points on a Circle," "Power of a Point, Radical Axis, and Radical Center," "Special Points and Special Lines in a Triangle," "Trigonometry, Areas, and Analytic Geometry," "Solid Geometry," and "Geometric Inequalities." Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty. The book concludes with a record of past IMO participation and award information, as well as an index of geometry problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.