Table of Contents

Introduction.

About the Author.

Chapter 1: Elementary Euclidean Geometry Revisited.

Review of Basic Concepts of Geometry.

Learning from Geometric Fallacies.

Common Nomenclature.

Chapter 2: Concurrency of Lines in a Triangle.

Introduction.

Ceva's Theorem.

Applications of Ceva's Theorem.

The Gergonne Point.

Chapter 3: Collinearity of Points.

Duality.

Menelaus's Theorem.

Applications of Menelaus's Theorem.

Desargues's Theorem.

Pascal's Theorem.

Brianchon's Theorem.

Pappus's Theorem.

The Simson Line.

Radical Axes.

Chapter 4: Some Symmetric Points in a Triangle.

Introduction.

Equiangular Point.

A Property of Equilateral Triangles.

A Minimum Distance Point.

Chapter 5: More Triangle Properties.

Introduction.

Angle Bisectors.

Stewart's Theorem.

Miquel's Theorem.

Medians.

Chapter 6: Quadrilaterals.

Centers of a Quadrilateral.

Cyclic Quadrilaterals.

Ptolemy's Theorem.

Applications of Ptolemy's Theorem.

Chapter 7: Equicircles.

Points of Tangency.

Equiradii.

Chapter 8: The Nine-Point Circle.

Introduction to the Nine-Point Circle.

Altitudes.

The Nine-Point Circle Revisited.

Chapter 9: Triangle Constructions.

Introduction.

Selected Constructions.

Chapter 10: Circle Constructions.

Introduction.

The Problem of Apollonius.

Chapter 11: The Golden Section and Fibonacci Numbers.

The Golden Ratio.

Fibonacci Numbers.

Lucas Numbers.

Fibonacci Numbers and Lucas Numbers in Geometry.

The Golden Rectangle Revisited.

The Golden Triangle.

Index.