Mathematical Olympiads 1998-1999: Problems and Solutions from Around the WorldTitu Andreescu, Zuming Feng This volume contains a large range of problems, with and without solutions, taken from 25 national and regional mathematics olympiads from around the world, and the problems are drawn from several years' contests. In many cases, more than one solution is given to a single problem in order to highlight different problem-solving strategies. The collection is intended as practice for students preparing for these competitions. Teachers and general readers looking for interesting problems will find also it very useful. |
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a₁ ABCD an+1 angle bisector B₁ C₁ circle circumcenter circumcircle circumradius claim color contains contradiction convex cubes cyclic quadrilateral denote desired digits distinct divides divisors edges elements equal equation exactly excircle exists Find function given implies incircle inequality inradius inside intersection lattice points law of cosines law of sines least lemma length Let ABC Mathematical Olympiad meet midpoint modulo n-tuples natural numbers nonempty nonnegative odd number orthocenter pairs parallel parallelepiped parallelogram perfect square perpendicular Pigeonhole Principle plane player polygon polynomial positive integers positive real numbers prime Problem 3 Let Prove rational real numbers rectangle respectively roots satisfy Second Solution segment sequence Show sides sin² subsets Suppose tangent theorem Titu Andreescu triangle ABC values vectors vertex vertices w₁ WLOG Xn+1