Geometry/Olympiad

The following is a list of olympiad geometry topics.

• 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

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.

See also

• Geometry
• Introductory Geometry
• Intermediate Geometry