Solving Problems In Geometry: Insights And Strategies For Mathematical Olympiad And Competitions

by Kim Hoo Hang, Haibin Wang

Overview

'This book is a useful reference for faculty members involved in contest preparation or teaching Euclidean geometry at the college level.'
MAA ReviewsThis new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems.This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.

Product Details

ISBN-13:	9789814583749
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	07/17/2017
Series:	Mathematical Olympiad Series , #10
Pages:	356
Sales rank:	919,141
Product dimensions:	5.90(w) x 8.90(h) x 0.80(d)

Table of Contents

Preface v

Chapter 1 Congruent Triangles 1

1.1 Preliminaries 1

1.2 Congruent Triangles 8

1.3 Circumcenter and Incenter of a Triangle 18

1.4 Quadrilaterals 22

1.5 Exercises 32

Chapter 2 Similar Triangles 35

2.1 Area of a Triangle 35

2.2 Intercept Theorem 47

2.3 Similar Triangles 55

2.4 Introduction to Trigonometry 63

2.5 Ceva's Theorem and Menelaus' Theorem 67

2.6 Exercises 83

Chapter 3 Circles and Angles 87

3.1 Angles inside a Circle 87

3.2 Tangent of a Circle 101

3.3 Sine Rule 110

3.4 Circumcenter, Incenter and Orthocenter 118

3.5 Nine-point Circle 125

3.6 Exercises 129

Chapter 4 Circles and Lines 133

4.1 Circles and Similar Triangles 133

4.2 Intersecting Chords Theorem and Tangent Secant Theorem 144

4.3 Radical Axis 154

4.4 Ptolemy's Theorem 165

4.5 Exercises 171

Chapter 5 Basic Facts and Techniques in Geometry 175

5.1 Basic Fuels 175

5.2 Basic Techniques 195

5.3 Constructing n Diagram 213

5.4 Exercises 226

Chapter 6 Geometry Problems in Competitions 229

6.1 Reverse Engineering 229

6.2 Recognizing a Relevant Theorem 238

6.3 Unusual and Unused Conditions 245

6.4 Seeking Clues from the Diagram 255

6.5 Exercises 270

Insights into Exercises 273

Solutions to Exercises 299