Solving Problems in Geometry

This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems.

This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.

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Contents:Congruent Triangles:PreliminariesCongruent TrianglesCircumcenter and Incenter of a TriangleQuadrilateralsExercisesSimilar Triangles:Area of a TriangleIntercept TheoremSimilar TrianglesIntroduction to TrigonometryCeva's Theorem and Menelaus' TheoremExercisesCircles and Angles:Angles inside a CircleTangent of a CircleSine RuleCircumcenter, Incenter and OrthocenterNine-point CircleExercisesCircles and Lines:Circles and Similar TrianglesIntersecting Chords Theorem and Tangent Secant TheoremRadical AxisPtolemy's TheoremExercisesBasic Facts and Techniques in Geometry:Basic FactsBasic TechniquesConstructing a DiagramExercisesGeometry Problems in Competitions:Reverse EngineeringRecognizing a Relevant TheoremUnusual and Unused ConditionsSeeking Clues from the DiagramExercises
Readership: Students, educators and general public interested in geometry and topology.
Keywords:Problem-solving;Mathematical Olympiad;GeometryReview:Key Features:There are currently very few books on the teaching of geometry in a systematic mannerThis book not only gives the solutions to geometrical problems, but also insights on how to search for clues and develop a strategy in tackling them. A large number of problems used in competitions are illustrated as examplesThe authors are active and experienced in the training of the national team for the International Mathematical Olympiad competitions