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I want to study geometry and was looking for some book that has lots of theorems and covers almost all Euclidean geometry that is needed for High School and Maths Olympiads. Thanks.

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    $\begingroup$ Not a book, but I suppose you've seen gogeometry. $\endgroup$ Jan 1, 2014 at 11:02
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    $\begingroup$ Didn't Euclid write one? $\endgroup$
    – dfeuer
    Jan 1, 2014 at 12:23

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Probably on of the best problem book which covers geometry, especially recommended for olympiads: http://students.imsa.edu/~tliu/Math/planegeo.pdf

http://www-math.mit.edu/~kedlaya/geometryunbound/geom-080399.pdf (contains many important synthetic methods with a bunch of exercises and examples).

http://hoaxung.files.wordpress.com/2010/04/marko-radovanovic-complex-numbers-in-geometry.pdf (great article which covers complex numbers stuff)

http://hoaxung.files.wordpress.com/2010/04/inversion_ddj-dusan-djukic.pdf (inversion)

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  • $\begingroup$ I dont want a problem book but instead some book that explains all of geometry...Although the problem book you have suggested is quite superb. $\endgroup$ Jan 4, 2014 at 10:00
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“A Beautiful Journey Through Olympiad Geometry” is a book that presents all the theorems/methods that you need to know in order to solve IMO problems. It contains solved problems using these theorems, but also related problems that are left unsolved as a practice for the reader. Check out the book preview and download the book (pay what you want) here.

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You can check following books:
1-Challenging Problems in Geometry
2-Geometry Revisited
3-Geometry Unbound

I actually got the links from artofproblemsolving site. You can find plenty of online material out there even on spesific topics of geometry.
Furthermore, it is highly curical that what level you are. You need to consider how much you studied and how far you want to go in geometry. Then, you need to pick carefully the book you want to study, regarding that information. Good luck.

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  • $\begingroup$ Although I know high school geometry, think of me as a person who does not even know what geometry means. $\endgroup$ Jan 1, 2014 at 14:05
  • $\begingroup$ The definition of your geometry level is pretty complicated. Nevertheless, you should first master on "proving things". I strongly suggest you to go through the proofs of elementary theorems in geometry. When you understand those proofs, you will feel stronger about geometry. You should take your time and digest them patiently. Then you may start solving olympiad problems. $\endgroup$
    – iamvegan
    Jan 1, 2014 at 14:34
  • $\begingroup$ Yes, that is what I want.Something with proofs of elementary theorems. $\endgroup$ Jan 1, 2014 at 15:04
  • $\begingroup$ So i may suggest you the first three chapters of geometry revisited. you can find some free djvu format from web. $\endgroup$
    – iamvegan
    Jan 1, 2014 at 15:18
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The best geometry book I know: http://www.mccme.ru/~akopyan/papers/EnGeoFigures.pdf

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  • $\begingroup$ That's nice, but do you know about some book that has quite a lot of geometry explained in a superb way... $\endgroup$ Jan 4, 2014 at 10:04
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Well there is a book "The Art and Craft Of Problem Solving" by Paul Zeitz. Its quite good, there is a section on Number theory and there is also a section on geometry. It will tell you of POP, etc. Wait! There is another book "Plane Euclidean Geometry: Theory and Problems" by A.D. Gardinier C.J. Bradley.

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