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Professor Zhang presents a new toolkit for solving geometry problems. He neatly presents these tools with 9 theorems and their elegant proofs. The cornerstone of his techniques is the "Area Method", based on the directed area of triangles and their relationship to proportional sides. Professor Zhang instructs his students to do the algebraic deduction and calculation while making reference to the figures and their geometric relationships. The advantages of this approach are not only that it looks straightforward but his proofs frequently rely on an almost fixed recipe. For this reason the methods are important in Automated Geometric Reasoning. The Area Method and Full Angle Method theorem provers are based on the techniques introduced in this book.

These methods have been used successfully by Chinese students training for the International Mathematical Olympiads. Throughout the book and all examples in the last two chapters present problems from various math competitions around the world, many from past International Mathematical Olympiads.

This book will be of great interest to students and coaches of mathematics competitions, and to researchers in Automated Geometric Reasoning.