Difference between revisions of "Geometry/Olympiad"

 
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The following is a list of olympiad [[geometry]] topics.
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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.
 
 
*  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]]
 
*  Miscellaneous
 
** [[Construction]]
 
** [[Locus]]
 
** [[3D Geometry]]
 
** [[Geometric inequalities]]
 
  
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== Topics ==
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=== Synthetic geometry ===
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* [[Cyclic quadrilaterals]]
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**[[Ptolemy's theorem]]
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* [[Orthic triangle]]
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* [[Incenter/excenter lemma]]
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* [[Directed angles]]
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* [[Similar triangles]]
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* [[Power of a point theorem]]
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* [[Radical axis]]
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* [[Ceva's theorem]]
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* [[Menelaus' theorem]]
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* [[Nine-point circle]]
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* [[Euler line]]
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* [[Simson line]]
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* [[Isogonal conjugates]] and [[Isotomic conjugates]]
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* [[Symmedians]]
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=== Analytic geometry ===
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* [[Trigonometry]]
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* [[Cartesian geometry]]
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* [[Linear algebra]]
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* [[Complex numbers]]
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* [[Barycentric coordinates]]
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=== Transformations ===
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* [[Homothety]]
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* [[Rotation]] and [[Reflection]]
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* [[Inversive geometry]]
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* [[Projective geometry]]
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**[[Brocard's Theorem]]
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**[[Pascal's Theorem]]
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* [[Spiral similarity]]
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=== Miscellaneous ===
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* [[Construction]]
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* [[Locus]]
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* [[3D Geometry]]
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* [[Geometric inequalities]]
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== Resources ==
 
== Resources ==
 
=== Books ===
 
=== Books ===
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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/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].
 
 
* [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 ==
* [[Geometry]]
 
 
* [[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

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