本书介绍了数学竞赛中几何不等式的基本证明方法和技巧，书中融合了作者多年来在几何不等式领域中的研究体会和培训学年的经验，高屋建瓴，深入浅出，书中的问题经过精心的选择，不少问题还是近年来初等几何不等式研究中的最新成果，书中大量引用学生的优秀解法，显现他们不同的思维视角，点评其解法的关键所在，捧读此书，你可感到这些年轻智者的创造风采，领略难题是怎样解成的诀窍。

Chapter 1 The method of segment replacement for distance inequalities
Chapter 2 Ptolemy's inequality and its application
Chapter 3 Inequality for the inscribed quadrilateral
Chapter 4 The area inequality for special polygons
Chapter 5 Linear geometric inequalities
Chapter 6 Algebraic methods
Chapter 7 Isoperimetric and extrernal value problem
Chapter 8 Embed inequality and inequality for moment of inertia
Chapter 9 Locus problem of Tsintsifas's inequality
Chapter 10 Shum's minimal circle problem
Chapter 11 Inequalities for tetrahedron
Answers and hints to selected exercises