Leng G. Geometric Inequalities 2015

Textbook in PDF format

"The examples are carefully picked and are useful for the method the author chose to highlight." Zentralblatt Math In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the Imo National Team to compete in the International Mathematical Olympiad. In the past ten years China's Imo Team has achieved outstanding results - they won the first place almost every year. The author is one of the coaches of China's Imo National Team, whose students have won many gold medals many times in Imo. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.
Preface
The method of segment replacement for distance inequalities
Ptolemy’s inequality and its application
Inequality for the inscribed quadrilateral
The area inequality for special polygons
Linear geometric inequalities
Algebraic methods
Isoperimetric and extremal value problem
Embed inequality and inequality for moment of inertia
Locus problem of Tsintsifas’s inequality
Shum’s minimal circle problem
Inequalities for tetrahedron
Answers and hints to selected exercises