Math book available at Amazon and many outlets

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Solutions for these following Mathematical Olympiad problems used to select the top math students in the world and nations are in the book titled The hard Mathematical Olympiad problems and their solutions by Steve Dinh, a.k.a. Vo Duc Dien published by AuthorHouse. This book will debut soon at Amazon.com and other sites. Note: Some mathematical symbols cannot be translated into this text editor and the reader may find them missing. Problem 1 of International Mathematical Talent Search Round 8 Prove that there is no triangle whose altitudes are of lengths 4, 7 and 10 units. Problem 2 of the Korean Mathematical Olympiad 2007 ABCD is a convex quadrilateral, and AB ≠ CD. Show that there exists a point M such that $latex \frac{AB}{CD}$ = $latex \frac{MA}{MD}$ = $latex \frac{MB}{MC}$. Problem 1 of Hong Kong Mathematical Olympiad 2002 Two circles intersect at points A and B. Through the point B a straight line is drawn, intersecting the first circle at K and the second circle at M. A line parallel to AM is tangent to the first circle at Q. The line AQ intersects the second circle again at R. a) Prove that the tangent to the second circle at R is parallel to AK. b) Prove that these two tangents are concurrent with KM. Problem 2 of the Irish Mathematical Olympiad 2010 Let ABC be a triangle and let P denote the midpoint of the side BC. Suppose that there exist two points M and N interior to the sides AB and AC, respectively such that |AD| = |DM| = 2|DN|, where D is the intersection point of the lines MN and AP. Show that |AC| = |BC|. Problem 2 of Hong Kong Mathematical Olympiad 2002 Find the value of sin²1° + sin²2° + … + sin²89°. Problem 3 of the Austrian Mathematical Olympiad 2001 In a convex pentagon, the areas of the triangles ABC, ABD, ACD and ADE are all equal to the same value F. What is the area of the triangle BCE?


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