Challenging Problems in Geometry (en Inglés) - Adam J. Wick

This book is intended as a beginner-friendly guide to plane geometry and is organized into three chapters.

The first chapter presents 36 important theorems in plane geometry, each accompanied by a proof. These theorems form a collection of fundamental tools that frequently appear in geometry problem solving. Selected examples are also included to illustrate how the theorems can be applied in practice. Readers are encouraged to study each theorem carefully and understand both its statement and proof before proceeding to the problem-solving sections of the book. A strong command of these results will make the later problems much more approachable.

The second chapter contains a collection of geometry problems, many of which are inspired by or drawn from mathematical competitions. This chapter gives readers an opportunity to put the ideas and techniques from the first chapter into practice. Readers are strongly encouraged to attempt each problem independently before consulting the solutions. Mathematics is best learned through active problem solving. Even when a problem cannot be solved completely, the effort spent exploring different approaches often leads to valuable insights and greater familiarity with important techniques.

Some of the problems in this book are challenging, and readers should not be discouraged if a solution does not come immediately. Struggling with a difficult problem is a natural and valuable part of learning mathematics. Very few students can solve every problem on their first attempt. What matters most is the willingness to think carefully, experiment with ideas, learn from unsuccessful approaches, and continue improving.

The third chapter provides complete solutions to the problems presented in Chapter Two. The solutions are written with clarity and accessibility in mind. Whenever possible, we have chosen direct and understandable approaches rather than unnecessarily complicated arguments. Our goal is not merely to present the final answer, but to help readers understand the reasoning and techniques behind each solution.

We hope that this book will help readers strengthen their knowledge of plane geometry, discover useful problem-solving techniques, and develop greater confidence in tackling challenging geometry problems. More importantly, we hope it encourages readers to enjoy the process of mathematical exploration and problem solving.

May this book be a helpful companion on your journey through geometry.

Enjoy your reading and problem solving!