[Math] A month for Olympiad-level geometry.

book-recommendationcontest-mathreference-requestsoft-question

In one month, I'll be writing a second round of a mathematical Olympiad.

My biggest concern is geometry. While I think I'm doing pretty well in number theory, algebra, combinatorics etc., I still can't say I really understood Olympiad geometry (and bashing is not always possible). Obviously, there are always problems one can and one can't solve, regardless of the training, but my question is:

What is the best books/set of exercises/article, that I could study from and get a greater grasp of Olympiad-level geometry a month before the competition?

I mean, a full month, $30$ days, no school or any other activities.

I must say, I'd prefer ones that don't use overly sophisticated notations and don't go into super-advanced theorems you happen to use once or never. And I'm aware that a month is not really a long time and this question may seem a bit like: "quickly, what should I learn to win an Olympiad". I don't mean it. I'm just asking – what to study Olympiad geometry from to greatest benefit while certainly greatly determined to?

EDIT: I'd like to address some comments regarding taking Olympiad too seriously. While I agree to great extent with this reasoning and I appreciate your concern, I'd like to clarify: it's not that I'm going to be working $\frac{24}7$ on maths only. I'd just like to work with the best resources available and thus not waste my time on exercises that aren't of much benefit to my geometry skills.

Best Answer

For an adequate update over a one-month period, I would suggest you:

  • "Euclidean Geometry in Mathematical Olympiads" by Evan Chen: this is a problem-solving book focused on Euclidean geometry, suitable and specifically written as a preparation for mathematical olympiads;

  • "Problems in Plane Geometry" by Igor F. Sharygin: it has several "non-standard" problems with increasing levels of difficulty, so that it is useful to understand some issues of plane geometry not often described in standard books, such as what additional constructions can be made, which "alternative" pathways could be used to arrive at the solution, and so on;

  • "Geometry Unbound" by Kiran S. Kedlaya, a very good paper structured in the form of a textbook, which starts from rudiments and arrives to the most modern areas of geometry, including inversion and projective geometry;

  • lastly, a complete book is "Problems in plane and solid geometry" by Viktor Prasolov (already cited in one of the comments), a comprehensive 600-page text with thousands of problems and detailed solutions covering all areas of plane and solid geometry.

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