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This challenging problem-solving book on Euclidean geometry requires nothing of the reader other than courage. Readers will encounter cyclic quadrilaterals, power of a point, homothety, and triangle centers, as well as such classical gems as the nine-point circle, the Simson line, and the symmedian. Both a traditional and a computational view of the use of complex numbers and barycentric coordinates is offered, while more advanced topics are covered in the final part. These include inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also how one would invent the solution to begin with. Providing over 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions, this book is especially suitable for students preparing for national or international mathematical Olympiads.

Cover:

Paperback

Edition Number:

1

ISBN:

9780883858394

Pages:

326

Author:

Chen Evan

Publisher:

MATHEMATICAL ASSOCIATION OF AMERICA

Release Year:

2016

Evan Chen is currently an undergraduate studying at the Massachusetts Institute of Technology. He won the 2014 USA Mathematical Olympiad, earned a gold medal at the IMO 2014 for Taiwan, and acts as a Problem Czar for the Harvard-MIT Mathematics Tournament.

Preface

Preliminaries

Part I. Fundamentals:

1. Angle chasing

2. Circles

3. Lengths and rules

4. Assorted configurations

Part II. Analytic Techniques:

5. Computational geometry

6. Complex numbers

7. Barycentric coordinates

Part III. Farther from Kansas:

8. Inversion

9. Projective geometry

10. Complete quadrilaterals

11. Personal favorites

Part IV. Appendices: Appendix A. An ounce of linear algebra

Appendix B. Hints

Appendix C. Selected solutions

Appendix D. List of contests and abbreviations

Bibliography

Index

About the author.