Difference between revisions of "Geometry/Olympiad"
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=== Synthetic geometry === | === Synthetic geometry === | ||
* [[Cyclic quadrilaterals]] | * [[Cyclic quadrilaterals]] | ||
| − | **[[Ptolemy's | + | **[[Ptolemy's theorem]] |
* [[Orthic triangle]] | * [[Orthic triangle]] | ||
| − | * [[Incenter/ | + | * [[Incenter/excenter lemma]] |
* [[Directed angles]] | * [[Directed angles]] | ||
* [[Radical Axis]] | * [[Radical Axis]] | ||
* [[Similar triangles]] | * [[Similar triangles]] | ||
| − | * [[Ceva's | + | * [[Ceva's theorem]] |
| − | * [[Menelaus' | + | * [[Menelaus' theorem]] |
* [[Nine-point circle]] | * [[Nine-point circle]] | ||
* [[Euler line]] | * [[Euler line]] | ||
Revision as of 16:02, 9 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
- 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.
