Geometry/Olympiad

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.

Topics

Synthetic geometry

• Cyclic quadrilaterals
  • Ptolemy's theorem
• 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

• Trigonometry
• Cartesian geometry
• Linear algebra
• Complex numbers
• Barycentric coordinates

Transformations

• Homothety
• Rotation and Reflection
• Circular inversion
• Projective geometry
  • Brocard's Theorem
  • Pascal's Theorem
• Spiral similarity

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.
• 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

• Introductory Geometry
• Intermediate Geometry