AMC and AIME geometry must-know techniques

Book Synopsis: One can say that the USA(J)MO qualification directly depends on student's geometry skills, as almost each year from about 33 percent to 47 percent of the AIME test consists of geometry problems. The main goal of this book is to teach the reader how to improve problem-solving skills of Geometry, and score better on the AMC (American Mathematics Competitions) and on the AIME (American Invitational Mathematics Examination). It includes several new techniques and theorems (some of them developed by the authors and never published before). It is intended as a teacher’s manual of mathematics, as a manual for math competition coaches, a self-study handbook for high-school students and mathematical competitors interested in the American Mathematics Competitions (especially AIME). The book teaches Geometry problem-solving strategies and includes a list of the most useful theorems and formulas needed to score better on the AMC and AIME, it also includes applications for each technique.

About the authors: Hayk Sedrakyan is an IMO medal winner, professional mathematical Olympiad coach in the greater Boston area, Massachusetts, USA. He has been the dean (and one of the main developers) of one of the biggest math competition preparation programs in the USA. He has been a Professor of mathematics in Paris and has a PhD in mathematics (optimal control and game theory) from the UPMC - Sorbonne University, Paris, France. Hayk is a Doctor of mathematical sciences in the USA, France, Armenia and holds three master’s degrees in mathematics from institutions in Germany, Austria, Armenia and has spent a small part of his PhD studies in Italy. He has worked as a scientific researcher for the European Commission, has been one of the Team Leaders at Harvard-MIT Mathematics Tournament (HMMT) and was an invited speaker at Imperial College London. He took part in the International Mathematical Olympiads (IMO) in United Kingdom, Japan, and Greece. Hayk has been elected as the President of the general assembly and a member of the management board of the Cite Internationale Universitaire de Paris (10,000 students, 162 different nationalities) and the same year they were nominated for the Nobel Prize. He is the son and was one of the students of Nairi Sedrakyan. Nairi Sedrakyan is involved in national and international Mathematics Olympiads having been the President of Armenian Mathematics Olympiads and a member of the IMO problem selection committee. Nairi Sedrakyan was the winner of Erdos Award 2022 (one of the highest international awards in mathematics) for contributing to the development of mathematics worldwide, in average 1 person per year (globally) wins this award. He is one of 3 people from the entire ex-USSR ever to win Erdos Award, the other 2 are: Grigori Perelman’s professor (the only person in the world who coached 2 Fields Medal winners) and Nikolay Konstantinov (founder of Tournament of the Towns). Nairi Sedrakyan is the author of one of the most difficult problems ever proposed in the history of the International Mathematical Olympiad (IMO), 5th problem of 37th IMO. This problem is considered to be one of the hardest problems ever in the IMO because none of the members of the strongest teams (national Olympic teams of China, USA, Russia) succeeded in solving it correctly and because the national Olympic team of China (the strongest team in IMO) obtained a cumulative result of 0 points and was ranked 6th instead of the usual 1st or 2nd place. The British 2014 film X+Y, released in the USA as A Brilliant Young Mind, inspired by the film Beautiful Young Minds (focuses on an English math genius chosen to represent the United Kingdom at IMO) also states that this problem is one of the hardest problems ever proposed in the history of IMO (minutes 9:40-10:30). His students have received 20 medals in the IMO, including Gold and Silver medals. Nairi Sedrakyan received a Gold Medal for contributions to World’s Mathematical Olympiads and Scientific Activities.