# Difference between revisions of "Geometry/Olympiad"

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− | + | An olympiad level study of [[geometry]] familiarity with intermediate topics to a high level, a multitude of new topics, and a highly developed proof-writing ability. | |

− | + | == Topics == | |

− | + | === Synthetic geometry === | |

− | + | * [[Cyclic quadrilaterals]] | |

− | + | **[[Ptolemy's Theorem]] | |

− | + | * [[Orthic triangle]] | |

− | + | * [[Incenter-Excenter Lemma]] | |

− | + | * [[Directed angles]] | |

− | + | * [[Radical Axis]] | |

− | + | * [[Similar triangles]] | |

− | + | * [[Ceva's Theorem]] | |

− | + | * [[Menelaus' Theorem]] | |

− | + | * [[Nine-point circle]] | |

− | + | * [[Euler line]] | |

− | + | * [[Simson line]] | |

− | + | * [[Isogonal conjugates]] and [[Isotomic conjugates]] | |

− | + | * [[Symmedians]] | |

− | + | === Analytic geometry ==== | |

− | + | * [[Trigonometry]] | |

− | + | * [[Linear algebra]] | |

− | + | * [[Complex numbers]] | |

− | + | * [[Barycentric coordinates]] | |

− | + | * [[Trilinear coordinates]] | |

− | + | === Transformations === | |

− | + | * [[Homothety]] | |

− | + | * [[Rotation]] and [[Reflection]] | |

− | + | * [[Inversive geometry]] | |

− | * | + | * [[Projective geometry]] |

− | + | **[[Brocard's Theorem]] | |

− | + | **[[Pascal's Theorem]] | |

− | + | === Miscellaneous === | |

− | + | * [[Construction]] | |

+ | * [[Locus]] | ||

+ | * [[3D Geometry]] | ||

+ | * [[Geometric inequalities]] | ||

+ | |||

== Resources == | == Resources == | ||

=== Books === | === Books === |

## Revision as of 17:37, 8 May 2021

An olympiad level study of geometry familiarity with intermediate topics to a high level, a multitude of new topics, and a highly developed proof-writing ability.

## Contents

## Topics

### Synthetic geometry

- Cyclic quadrilaterals
- Orthic triangle
- Incenter-Excenter Lemma
- Directed angles
- Radical Axis
- Similar triangles
- Ceva's Theorem
- Menelaus' Theorem
- Nine-point circle
- Euler line
- Simson line
- Isogonal conjugates and Isotomic conjugates
- Symmedians

### Analytic geometry =

### Transformations

### Miscellaneous

## Resources

### Books

- Euclidean Geometry In Mathematical Olympiads by Evan Chen
- Geometry Revisited -- A classic.
- Geometry of Complex Numbers by Hans Schwerdtfeger.
- Geometry: A Comprehensive Course by Dan Pedoe.
- Non-Euclidean Geometry by H.S.M. Coxeter.
- Projective Geometry by H.S.M. Coxeter.

See math books for additional texts.

### Classes

- The Olympiad Geometry class, an Olympiad level course over geometry.
- The Worldwide Online Olympiad Training (WOOT) Program -- Olympiad training in various subjects including geometry.