Imo Problems, Theorems, and Methods: Geometry

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 this book, we categorize IMO geometry problems 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 introduces relevant basic knowledge and methods, accompanied by some typical examples.The IMO questions in the chapters are classified according to the knowledge, methods, and characteristics involved, arranged in chronological order. Various good solutions are provided for some questions. The difficulty of the questions is statistically analyzed, and the scoring situation of the Chinese team is explained. At the end of the book, there is information on previous IMO competitions and awards, as well as an index of geometry test questions, which is convenient for readers to refer to and further study.