# Difference between revisions of "Geometry/Olympiad"

Etmetalakret (talk | contribs) |
Etmetalakret (talk | contribs) |
||

Line 8: | Line 8: | ||

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

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

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

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

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

− | |||

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

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

## Revision as of 10:56, 10 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.