# Difference between revisions of "Geometry/Olympiad"

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− | + | An olympiad level study of [[geometry]] involves 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]] | ||

+ | * [[Similar triangles]] | ||

+ | * [[Power of a point theorem]] | ||

+ | * [[Radical axis]] | ||

+ | * [[Ceva's theorem]] | ||

+ | * [[Menelaus' theorem]] | ||

+ | * [[Nine-point circle]] | ||

+ | * [[Euler line]] | ||

+ | * [[Simson line]] | ||

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

+ | * [[Symmedians]] | ||

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

+ | * [[Trigonometry]] | ||

+ | * [[Cartesian geometry]] | ||

+ | * [[Linear algebra]] | ||

* [[Complex numbers]] | * [[Complex numbers]] | ||

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

− | *[[Barycentric | + | === Transformations === |

− | + | * [[Homothety]] | |

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

− | * [[ | + | * [[Inversive geometry]] |

− | * [[ | ||

− | |||

− | * [[ | ||

* [[Projective geometry]] | * [[Projective geometry]] | ||

− | |||

− | |||

**[[Brocard's Theorem]] | **[[Brocard's Theorem]] | ||

**[[Pascal's Theorem]] | **[[Pascal's Theorem]] | ||

− | * [[ | + | * [[Spiral similarity]] |

− | * [[ | + | === Miscellaneous === |

− | * [[ | + | * [[Construction]] |

− | * [[ | + | * [[Locus]] |

− | + | * [[3D Geometry]] | |

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

+ | |||

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

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

+ | *[https://www.amazon.com/Euclidean-Geometry-Mathematical-Olympiads-Problem/dp/0883858398/ref=cm_cr_arp_d_product_top?ie=UTF8 Euclidean Geometry In Mathematical Olympiads] by [[Evan Chen]] | ||

* [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic. | * [http://www.amazon.com/exec/obidos/ASIN/0883856190/artofproblems-20 Geometry Revisited] -- A classic. | ||

− | * [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans | + | * [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerdtfeger. |

* [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe. | * [http://www.amazon.com/exec/obidos/ASIN/0486658120/artofproblems-20 Geometry: A Comprehensive Course] by Dan Pedoe. | ||

* [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]]. | * [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]]. | ||

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=== Classes === | === Classes === | ||

− | * The [http://www.artofproblemsolving.com/school/course/olympiad-geometry Olympiad | + | * The [http://www.artofproblemsolving.com/school/course/olympiad-geometry Olympiad Geometry] class, an Olympiad level course over geometry. |

− | * The [http://www.artofproblemsolving.com/school/course/woot Worldwide Online Olympiad Training (WOOT) Program] -- Olympiad training in | + | * The [http://www.artofproblemsolving.com/school/course/woot Worldwide Online Olympiad Training (WOOT) Program] -- Olympiad training in various subjects including geometry. |

== See also == | == See also == |

## Latest revision as of 11:59, 11 May 2021

An olympiad level study of geometry involves 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
- Similar triangles
- Power of a point theorem
- Radical axis
- 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.