As a 10th grader who'll take the ICSE exam in Q1 2024, I am planning to attempt the Indian Olympiad Qualifier in Mathematics next year, and quite hopefully RMO, INMO, and IMO afterward. I have found good sources to learn about other topics like number theory, algebra, and combinatorics. However, I am struggling to find books from where I can learn about Olympiad geometry. Any recommendations for books that explain the theoretical aspects of geometry and combinatorial geometry properly?
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3$\begingroup$ There seem to be a lot of geometry books on Amazon after a quick Google search. That is if you want to go out of your way to spend some money. $\endgroup$– AcceleratorCommented Jun 1, 2023 at 21:05
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$\begingroup$ awesomemath.org/shop/about-awesomemath-books I see, books shown at awesomemath.org/shop and here is one: awesomemath.org/product/introduction-to-olympiad-geometry $\endgroup$– Will JagyCommented Jun 1, 2023 at 21:21
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2 Answers
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The classical reference is
- Euclidean Geometry in Mathematical Olympiads by Evan Chen (you can find virtually all solutions at AOPS).
In post-Soviet countries, we also appreciate
- Problems in Plane Geometry by V. Prasolov. Maybe it's outdated to meet the current IMO level, but it is definitely worth a look, at least because it has full solutions to all problems (many of which are timeless classics) of a broad range of topics.
- Geometry in Figures by A. Akopyan (a more modern and a way more difficult book.)
Going through these books in combination with solving olympiad problems from national olympiads worldwide as well as reading specialised handouts and articles on geometry (you can find them, say, at AOPS) will be enough to succeed at most olympiads.
P.S. Don't overlearn theory: olympiad geometry is basically about little tricks that you gain after practice. In real life, (accessible) national-level problems usually involve nothing more than basic things like angle chasing. Heavy machinery is needed are usually required for the most difficult tasks in a set, but you won't be able to solve them unless you master the basics.
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Euclidean Geometry in Mathematical Olympiads by Evan Chen is definitely a must read, it contains most of the knowledge essential for olympiads, and also comes with lots of problems and hints
Besides that, Geometry Unbound by Kiran Kedlaya and Lemmas in Olympiad Geometry by Titu Andrescu are also nice books.
