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 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.

Tianqi Lin is a mathematics teacher at High School Affiliated to Fudan University, engaged in mathematics education research, and enjoys solving and creating problems in plane geometry. He has participated in the proposition work of the Chinese national training team for the International Mathematical Olympiad in 2019, 2018, and 2016, and have participated in the proposition work of various competitions multiple times. He is passionate about communication, and has published articles in publications such as "Intermediate Mathematics" to exchange ideas with readers on solving and proposing plane geometry problems.

Bin Xiong is a professor and doctoral supervisor at the School of Mathematical Sciences, East China Normal University, director of the Shanghai Key Laboratory of Core Mathematics and Practice, and director of the International Mathematical Olympiad Research Center. He is an expert with special allowance from the State Council, awarded the Shanghai May Day Labor Medal, and recognized as a model teacher and educator in Shanghai. More than 100 papers have been published both domestically and internationally, and over 150 books have been edited and co-authored. He served as the leader and head coach of the Chinese team at the International Mathematical Olympiad more than 10 times and received the Paul Erdos Award for International Mathematics in 2018.

About the Translator

Xinyuan Yang is a PhD from School of Mathematical Sciences, East China Normal University. His research focuses on mathematics education and mathematics competitions. During the doctoral period, he was sent to the University of Haifa for one year by the officially-sponsored study abroad program. Over the years, he has maintained a keen interest in mathematical competitions, especially in geometry and number theory. He served as an external mentor for mathematics competition courses at several high schools and participated multiple times in the grading work for major mathematics competitions in China.