Geometry

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Lecture notes on Geometry (for Math Olympiad — IOQM, RMO, INMO)

Click on the links below to download.

• Triangles
• Congruence and similarity of triangles
• Parallelograms
• Pythagoras’ theorem
• Pythagorean triples
• Triangle centers
  • Centroid
  • Circumcenter
  • Incenter
  • Orthocenter
  • Miscellaneous
• Concurrency and Collinearity
• Central lines
• Circles
• Power of a point and radical axis
• Cyclic quadrilaterals
• Using complex numbers

• Click here to download Algebra notes.
• Click here to download Combinatorics notes.
• Click here to download Number Theory notes.

These notes

• may be useful
  • to the students who would like to have a look at some of the past RMO problems, in order to have an idea of the notions/topics involved, and/or to have a glimpse before getting started, or just curious about it,
  • to the students, who would like to prepare and would like to have the relevant questions organized across the topics and sub-topics,
• also aim
  • to spread awareness for the Mathematics Olympiad programme in India, conducted by the Homi Bhabha Centre for Science Education (HBCSE), which is the only programme in India leading to participation in the following International Mathematical Olympiads — IMO, APMO, EGMO. No other contests are recognized.
  • to provide resources to the students who may not have access to introductory/preparatory materials related to Mathematics Olympiad.

References/Resources

• Olympiad Training Materials from IMOmath
• A Beautiful Journey Through Olympiad Geometry by Stefan Lozanovski
• Euclidean Geometry in Mathematical Olympiads (EGMO) by Evan Chen. The Automatically Generated EGMO Solutions Treasury contains updated solutions to a significant number of the sourced problems.
• A video by Zlatko Salko Lagumdžija.