# Difference between revisions of "Geometry/Olympiad"

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* [[Incenter/excenter lemma]] | * [[Incenter/excenter lemma]] | ||

* [[Directed angles]] | * [[Directed angles]] | ||

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

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

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

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

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

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

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

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

=== Miscellaneous === | === Miscellaneous === | ||

* [[Construction]] | * [[Construction]] | ||

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* [http://www.amazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerdtfeger. | * [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/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]]. | * [http://www.amazon.com/exec/obidos/ASIN/0387406239/artofproblems-20 Projective Geometry] by [[H.S.M. Coxeter]]. | ||

See [[math books]] for additional texts. | See [[math books]] for additional texts. | ||

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

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* [[Geometry/Introduction | Introductory Geometry]] | * [[Geometry/Introduction | Introductory Geometry]] | ||

* [[Geometry/Intermediate | Intermediate Geometry]] | * [[Geometry/Intermediate | Intermediate Geometry]] |

## Latest revision as of 16:25, 18 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.
- 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.