Difference between revisions of "Geometry/Olympiad"

Line 1: Line 1:
The following is a list of olympiad [[geometry]] topics.
+
An olympiad level study of [[geometry]] familiarity with intermediate topics to a high level, a multitude of new topics, and a highly developed proof-writing ability.
  
Synthetic geometry
+
== Topics ==
** [[Cyclic quadrilaterals]]
+
=== Synthetic geometry ===
***[[Ptolemy's Theorem]]
+
* [[Cyclic quadrilaterals]]
** [[Orthic triangle]]
+
**[[Ptolemy's Theorem]]
** [[Incenter-Excenter Lemma]]
+
* [[Orthic triangle]]
** [[Directed angles]]
+
* [[Incenter-Excenter Lemma]]
** [[Radical Axis]]
+
* [[Directed angles]]
** [[Similar triangles]]
+
* [[Radical Axis]]
** [[Ceva's Theorem]]
+
* [[Similar triangles]]
** [[Menelaus' Theorem]]
+
* [[Ceva's Theorem]]
** [[Nine-point circle]]
+
* [[Menelaus' Theorem]]
** [[Euler line]]
+
* [[Nine-point circle]]
** [[Simson line]]
+
* [[Euler line]]
** [[Isogonal conjugates]] and [[Isotomic conjugates]]
+
* [[Simson line]]
** [[Symmedians]]
+
* [[Isogonal conjugates]] and [[Isotomic conjugates]]
Analytic geometry
+
* [[Symmedians]]
** [[Trigonometry]]
+
=== Analytic geometry ====
** [[Linear algebra]]
+
* [[Trigonometry]]
** [[Complex numbers]]
+
* [[Linear algebra]]
** [[Barycentric coordinates]]
+
* [[Complex numbers]]
** [[Trilinear coordinates]]
+
* [[Barycentric coordinates]]
Transformations
+
* [[Trilinear coordinates]]
** [[Homothety]]
+
=== Transformations ===
** [[Rotation]] and [[Reflection]]
+
* [[Homothety]]
** [[Inversive geometry]]
+
* [[Rotation]] and [[Reflection]]
** [[Projective geometry]]
+
* [[Inversive geometry]]
* Miscellaneous
+
* [[Projective geometry]]
** [[Construction]]
+
**[[Brocard's Theorem]]
** [[Locus]]
+
**[[Pascal's Theorem]]
** [[3D Geometry]]
+
=== Miscellaneous ===
** [[Geometric inequalities]]
+
* [[Construction]]
 +
* [[Locus]]
 +
* [[3D Geometry]]
 +
* [[Geometric inequalities]]
  
 +
 
== Resources ==
 
== Resources ==
 
=== Books ===
 
=== Books ===

Revision as of 17:37, 8 May 2021

Invalid username
Login to AoPS